‘Well-heeled’ means wealth or well provided for. The word “heeled” has several meanings.
‘Well provided with money’ is our contemporary understanding, so that has to be a good place to start. In Eva Wilder Brodhead’s Bound in Shallows, 1897, there’s the line: “I ain’t so well-heeled right now.”
The context of the story makes it clear that this ‘not so well-heeled’ refers to poverty. Good quality shoes have never been available to the poor and consequently, have been seen as an indication of prosperity. It’s reasonable to assume that the heel being referred to here is the heel of a shoe or boot, as in the converse of the phrase, ‘down at heel’.
The ‘having a heel’ version is cited in the Iowa newspaper the Dubuque Daily Herald, April 1866.
The above citations, as well as the large majority of other early references, are American and it’s reasonable to suggest that the term originated in the USA. If we take a broad view and say that the phrase meant ‘well equipped’ (with something), we could accept any of the above as plausible origins.