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A side goal was being able to print every iteration of the board: just remove the middle ; in while(g.i()) ; System.out.print(g.s());. Unfortunately, in this version, gravity works in strangely. Each pass I take the first non-stuck ball and move it. Short circuiting iterate() there is less bytes than going over the whole board then returning if anything changed.

A side goal was being able to print every iteration of the board: just remove the middle ; in while(g.i()) ; System.out.print(g.s()); (Though this does disable the last print which has the 0->power conversion). Unfortunately, in this version, gravity works in strangely. Each pass I take the first non-stuck ball and move it. Short circuiting iterate() there is less bytes than going over the whole board then returning if anything changed.

Java, Too Many 1102 bytes

Realistically, this could be golfed further. I was more interested in implementing the spec, however. I'll take another stab at golfing it tomorrow (maybe even make it into triple digits ^.^).

class G{static class T{final char s;int p=0;T(char c){s=c;}}static T F=new T('-');static T R=new T('\\');static T L=new T('/');static T W=new T('#');static T A=new T(' ');static class B{T[][]o;B(T[][]t){o=t;}boolean i(){boolean r=1<0;for (int i=o.length-2; i>0; i--)for (int j=0; j<o[i].length; j++)if (o[i][j].p>0)if (m(i,j,i+1,j)||o[i+1][j]==L&&m(i,j,i+1,j-1)||o[i+1][j]==R&&m(i,j,i+1,j+1))r = 1>0;else o[i][j]=new T((o[i][j].p+"").charAt(0));return r;}boolean m(int a, int b, int c, int d){if (o[c][d]==A||o[c][d].p>0){o[a][b].p+=o[c][d].p;o[c][d]=o[a][b];o[a][b]=A;return 1>0;}return 1<0;}public String toString(){String s="";for(T[]r:o){for(T t:r)s+=t.s;s+="\n";}return s;}}static B p(String s) {String[]r=s.split("\\\\n");T[][]b=new T[r.length][r[0].length()];for(int i=0;i<b.length;i++)for(int j=0;j<b[i].length;j++)switch(r[i].charAt(j)){case'-':b[i][j]=F;break;case'\\':b[i][j]=R;break;case'/':b[i][j]=L;break;case'o':b[i][j]=new T('o'){{p=1;}};break;case'#':b[i][j]=W;break;default:b[i][j]=A;}return new B(b);}public static void main(String[]a){B b=p(a[0]);while(b.i());System.out.print(b);}}

A side goal was being able to print every iteration of the board: just remove the middle ; in while(b.i()) ; System.out.print(b);.

java -jar G.jar "##########\n# \      #\n#o       #\n#  - -\o #\n#/-    \ #\n#  \oo-/\#\n#-/ \   /#\n#   \ \  #\n#       /#\n##########"

public class GravitySimulator {
    static class Token {
        static Token FLOOR = new Token('-');
        static Token SLIDE_RIGHT = new Token('\\');
        static Token SLIDE_LEFT = new Token('/');
        static Token WALL = new Token('#');
        static Token AIR = new Token(' ');

        final char symbol;
        int power=0;
        Token(char s) {symbol=s;}
    }

    static class Board {
        Token[][] board;
        Board(Token[][] tokens) {
            board = tokens;
        }

        boolean iterate() {
            boolean didSomething = false;

            for (int i=board.length-2; i>0; i--) {
                for (int j=0; j<board[i].length; j++) {
                    if (board[i][j].power>0) {
                        if (move(i,j,i+1,j) || board[i+1][j]==Token.SLIDE_LEFT && move(i,j,i+1,j-1) || board[i+1][j]==Token.SLIDE_RIGHT && move(i,j,i+1,j+1))
                            didSomething = true;
                        else board[i][j] = new Token(Integer.toString(board[i][j].power).charAt(0));
                    }
                }
            }
            return didSomething;
        }

        boolean move(int x1, int y1, int x2, int y2) {
            if (board[x2][y2] == Token.AIR || board[x2][y2].power>0) {
                board[x1][y1].power += board[x2][y2].power;
                board[x2][y2] = board[x1][y1];
                board[x1][y1] = Token.AIR;
                return true;
            } else return false;
        }

        @Override
        public String toString() {
            String s = "";
 
            for (Token[] row : board) {
                for (Token token : row) {
                    s+=token.symbol;
                }
                s+="\n";
            }
 
            return s;
        }
    }

    static Board fromString(String s) {
        String[] rows = s.split("\\\\n");
        Token[][] board = new Token[rows.length][rows[0].length()];
        for (int i=0; i<board.length; i++) {
            for (int j=0; j<board[i].length; j++) {
                switch(rows[i].charAt(j)) {
                    case '-': board[i][j]=Token.FLOOR;break;
                    case '\\':board[i][j]=Token.SLIDE_RIGHT;break;
                    case '/': board[i][j]=Token.SLIDE_LEFT;break;
                    case 'o': board[i][j]=new Token('o'){{power=1;}};break;
                    case '#': board[i][j]=Token.WALL;break;
                    default:  board[i][j]=Token.AIR;
                }
            }
        }
        return new Board(board);
    }

    public static void main(String[] args) {
        Board b = fromString(args[0]);
        while(b.iterate());
        System.out.println(b);
    }
}

(I should mention that the Readable version has one difference in logic: the Token constants are inside the Token class in the readable and outside in the golfed.)

Obvious things to hit:

• Board class can go
• Probably can lose some of the statics
• Use custom 1 letter toString (3 bytes)
• Kill the final (6 bytes)
• Maybe if I can do this without class Token I can make this a function and save the class overhead

(I'm to lazy to fix these right now I'll come back tomorrow)

{Found an error case, fixing currently}

Java, Too Many 1102 987 bytes

\o/ It's under 1000!

class G{class T{char s;int p=0;T(char c){s=c;}}T A=new T(' ');T[][]o;boolean i(){for(int i=1;i<o.length;i++)for(int j=1;j<o[i].length;j++)if(o[i][j].p>0){if(m(i,j,i+1,j)||o[i+1][j].s=='/'&&m(i,j,i+1,j-1)||o[i+1][j].s=='\\'&&m(i,j,i+1,j+1))return 1>0;int w=o[i][j].p;o[i][j]=new T(Integer.toString(w).charAt(0)){{p=w;}};}return 1<0;}boolean m(int a,int b,int c,int d){if(o[c][d]==A||o[c][d].p>0){o[a][b].p+=o[c][d].p;o[c][d]=o[a][b];o[a][b]=A;return 1>0;}return 1<0;}String s(){String s="";for(T[]r:o){for(T t:r)s+=t.s;s+="\n";}return s;}void f(String s){String[]r=s.split("\\\\n");o=new T[r.length][r[0].length()];for(int i=0;i<o.length;i++)for(int j=0;j<o[i].length;j++)switch(r[i].charAt(j)){case'-':o[i][j]=new T('-');break;case'\\':o[i][j]=new T('\\');break;case'/':o[i][j]=new T('/');break;case'o':o[i][j]=new T('o'){{p=1;}};break;case'#':o[i][j]=new T('#');break;default:o[i][j]=A;}}public static void main(String[]a){G g=new G();g.f(a[0]);while(g.i());System.out.println(g.s());}}

A side goal was being able to print every iteration of the board: just remove the middle ; in while(g.i()) ; System.out.print(g.s());. Unfortunately, in this version, gravity works in strangely. Each pass I take the first non-stuck ball and move it. Short circuiting iterate() there is less bytes than going over the whole board then returning if anything changed.

java -jar G.jar "##########\n# o-/    #\n#-  / -/ #\n# oo   o #\n# /   \o #\n# o   o \#\n#    o   #\n#   -\o  #\n#\  \\ o/#\n##########"

class GravitySimulator {
    class Token {
        char symbol;
        int power = 0;

        Token(char c) {
            symbol = c;
        }
    }

    Token A = new Token(' ');

    Token[][] board;

    boolean iterate() {
        for (int i=1; i<board.length; i++)
            for (int j=1; j<board[i].length; j++) 
                if (board[i][j].power>0) {
                    if (move(i,j,i+1,j) || board[i+1][j].symbol=='/' && move(i,j,i+1,j-1) || board[i+1][j].symbol=='\\' && move(i,j,i+1,j+1)) return true;
                    int pow = board[i][j].power;
                    board[i][j] = new Token(Integer.toString(pow).charAt(0)){{power=pow;}};
                }
        return false;
    }

    boolean move(int x1, int y1, int x2, int y2) {
        if (board[x2][y2] == A || board[x2][y2].power>0) {
            board[x1][y1].power += board[x2][y2].power;
            board[x2][y2] = board[x1][y1];
            board[x1][y1] = A;
            return true;
        } return false;
    }

    String string() {
        String s = "";
        for (Token[] row : board) {
            for (Token token : row) s+=token.symbol;
            s+="\n";
        }
        return s;
    }

    void fromString(String s) {
        String[] rows = s.split("\\\\n");
        board = new Token[rows.length][rows[0].length()];
        for (int i=0; i<board.length; i++) 
            for (int j=0; j<board[i].length; j++) 
                switch(rows[i].charAt(j)) {
                    case '-': board[i][j]=new Token('-');break;
                    case '\\':board[i][j]=new Token('\\');break;
                    case '/': board[i][j]=new Token('/');break;
                    case 'o': board[i][j]=new Token('o'){{power=1;}};break;
                    case '#': board[i][j]=new Token('#');break;
                    default:  board[i][j]=A;
                }
    }

    public static void main(String[] args) {
        GravitySimulator g = new GravitySimulator();
        g.fromString(args[0]);
        while(g.iterate());
        System.out.println(g.string());
    }
}

{Found an error case, fixing currently}