Rockstar, 82 73 66 bytes

listen to S
cut S
O's ""
while S
roll S into C
let O be+C*2

say O

Try it here (Code will need to be pasted in)

Rockstar, 82 73 66 57 bytes

listen to S
cut S
O's ""
while S
let O be+roll S*2

say O

Try it here (Code will need to be pasted in)

listen to S     :Read input string into variable S
cut S           :Split into an array
O's ""          :Initialise O as an empty string
while S         :While S is not empty
let O be+       :  Append to O
  roll S        :    Pop the first element from S
  *2            :    Duplicate
                :End while loop
say O           :Output O

Rockstar, 82 73 bytes

listen to S
cut S
X's0
while S-X
let S at X be*2
let X be+1

join S
say S

Try it here (Code will need to be pasted in)

Rockstar, 82 73 66 bytes

listen to S
cut S
O's ""
while S
roll S into C
let O be+C*2

say O

Try it here (Code will need to be pasted in)

Rockstar, 82 bytes

listen to S
O's""
X's0
while S at X
let C be S at X
let O be+C+C
let X be+1

say O

Try it here (Code will need to be pasted in)

Rockstar, 82 73 bytes

listen to S
cut S
X's0
while S-X
let S at X be*2
let X be+1

join S
say S

Try it here (Code will need to be pasted in)