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Mathematica, 123 119 118 bytes

f=FromCharacterCode[s=SortBy;#&@@@s[Join@@(s[Tally@ToCharacterCode@#,-Last@#&]/.{x_,n_}:>({x,#/n}&~Array~n)),{Last}]]&

Defines a named function f. Ungolfed:

f = FromCharacterCode[
   s = SortBy;
   # & @@@ s[
     Join @@ (
       s[
         Tally@ToCharacterCode@#,
         -Last@# &
         ] /. {x_, n_} :> ({x, #/n} &~Array~n)
       ),
     {Last}
     ]
   ] &

Using built-in rational types seemed like a good idea for this. Of course, this is nowhere near CJam. Basically, I'm representing the grid shown in the challenge as a list of pairs. The first thing in the pair is the character code, the second is it's position as a fraction less than or equal to 1 (the final column being 1). Having made sure that the individual characters are already in the right order, I just need to sort this stably by said fraction to get the desired result.