A little-used definition of heeled is wealthy. So the phrase well-heeled describes someone who has money or is well provided for.
No one knows the exact origins of heeled in this use, but there are a few theories. One is that this sense of heeled has to do with shoes; a person who has nice shoes is well-heeled and hence well-off. Or our modern sense of well-heeled could come from mid-19th-century American-West slang, where well-heeled meant armed with a gun.
Well-healed makes sense in its own right, but it has nothing to do with being wealthy. Obviously, it describes someone who has healed well.
Tens of thousands of Greeks—from the well-heeled to the less well-off—have moved their savings out of the country. [Wall Street Journal]
Opening with expletives that perhaps kept the usual well-heeled opera crowd away, the plot whips along at a dizzying pace. [Herald Scotland]
I remember when the passion for Clinique non-allergenic cosmetics swept the consciousness of our well-heeled eleganzia. [Herald Sun]
He lives with wife Carolyn in a beautiful big home in a well-heeled area of West Vancouver. [Vancouver Sun]