Middle has not come up with more details yet (and so far is only familiar with Peter Jackson's take, not the originals -- I suspect Middle doesn't realize that elves can be the bad guys too, so we'll see what happens when they finally read Silmarillion).

If I were going to run with this theory based on MCU and Tolkien bookverse, I'd say that Steve's scrawniness as a young child was not necessarily because of illness (though perhaps there was a poisoning involved) but simply because his growth rate was that of the Eldar rather than the Edain, and the serum finished out his growth process. Everyone who's tried to recreate Erskine's serum since then has gotten it right; it's just that all the other people it's been used on have been Edain.

(And at the end of Endgame when Steve went back to be with Peggy he absolutely chose to accept the Gift of Men.)