Capped string ladder
Jelly, 6 bytes

JṡFṢị⁸


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How it works

JṡFṢị⁸  Main link. Arguments: s (string), n (integer)

J       Get the indices of s.
 ṡ      Split the indices into overlapping chunks of length n.
  F     Flatten the array of chunks.
   Ṣ    Sort the resulting array of indices.
    ị⁸   Get the characters of s at these indices.


Sample run

JṡFṢị⁸  "abalone", 3

J       [1, 2, 3, 4, 5, 6, 7].
 ṡ      [[1, 2, 3], [2, 3, 4], [3, 4, 5], [4, 5, 6], [5, 6, 7]]
  F     [1, 2, 3, 2, 3, 4, 3, 4, 5, 4, 5, 6, 5, 6, 7]
   Ṣ    [1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7]
    ị⁸  "abbaaalllooonne"