There are several meanings of the word heeled. Three of these can lay some claim to being the source of this phrase:
- Provided with money.
- Equipped with a weapon, especially a revolver.
- Having a heel, or spur.
Of course, '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 'equipped with a revolver' meaning is given in J. H. Beadle's Undeveloped West, 1873:
"To travel long out West a man must be, in the local phrase, 'well heeled'."
Again, the context that the line is in makes the meaning clear - in this case the possession of a gun.
The 'having a heel' version is cited in the Iowa newspaper the Dubuque Daily Herald, April 1866:
"... they resembled dung hill chickens thrown into the pit with their natural spurs, to meet and contend with game cocks well heeled. One stoke puts them to flight, squawking as they go; they cannot stand steel."
Here, the heel is clearly an applied spur that cocks were equipped with during cock-fights.
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. The cock-fighting citation is the earliest, but not so much earlier than the others to make it the obvious source.
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. Unless more evidence is found that link any one them to the phrase as we now understand it we have to say that, apart from locating the origin in the USA, the jury is still out on this one.