http://www.word-detective.com/072999.html

As regards your question, however, I'm afraid that you and your hyper-matriculated pal are
going to have to buy your own dinners. No one knows for certain where the "skate" in
"cheapskate" (meaning a very stingy person) came from, although we do know that
"cheapskate" first appeared in English around 1896. Authorities are also fairly certain that this
kind of "skate" is not related to the "skate" fish, which resembles a ray and takes its name from
the Old Norse word "skata." The other common kind of "skate" (as in roller-skate or ice-skate)
is also not related to "cheapskate," and comes from an Old French word ("eschasse") meaning
"stilts." Go figure.

The most plausible theory about the "skate" in "cheapskate" traces it to the Scots word "skate,"
a term of contempt which apparently also crops up in a slightly different form in the archaic
term "blatherskite," meaning a person who blathers, or babbles nonsense. If this theory is true,
"cheapskate" would thus translate as essentially "stingy creep," which makes sense.

Unfortunately, that's about all we know about this particular "skate." So I guess we'll never
know whether your friend would have taken you to a good restaurant, or whether he'd have
turned out to be (drum roll, please) a cheapskate.