I say “merry,” “Mary,” and “marry” identically. I first noticed there was a difference for some people when I learned the tongue-twisting song “Mary Mac,” which has the chorus
Mary Mac’s mother’s making Mary Mac marry me.
My mother’s making me marry Mary Mac.
I’m gonna marry Mary for my Mary to take care of me.
We’ll all be makin’ merry when I marry Mary Mac.
On the recorded version I have, “merry” and “Mary” are the same (like “berry”) but “marry” has a long ‘a’ (almost like “father”). The singers are from N. Ireland and Germany, though, so not examples of an American variation.