Write a program to elasticize strings

Jelly, 3 bytes

Code:

ĖP€

Explanation:

Ė     # Enumerate.
 P€   # Product of each.
      # Implicit joining of everything.

Uses the Jelly encoding. Try it online!.

J, 4 bytes

#~#\

Usage

   f =: #~#\
   f 'Why'
Whhyyy
   f 'SKype'
SKKyyyppppeeeee
   f 'LobbY'
LoobbbbbbbYYYYY
   f 'A and B'
A  aaannnnddddd      BBBBBBB

Explanation

#~#\  Input: s
  #\  Computes the length of each prefix of s
      This forms the range [1, 2, ..., len(s)]
#~    For each value in the range, copy the character at the
      corresponding index that many times
      Return the created string

Brainfuck, 15 bytes

,[>+[->+<<.>],]

Pretty straightforward implementation, shifting the memory space by 1 for each input char. Requires an interpreter that gives 0 on EOF, and 32-bit/arbitrary precision cells for inputs longer than 255 chars.

Try it online! (Note: TIO uses 8-bit cells)