@Adverb,
"... the size of basketballs" usually means "big." There are a lot of measurements that seem to take the form of balls used for sports -- golfballs, baseballs, etc. A "basketball," in this progression, is the biggest one.
So the person is saying that they have a lot of scruples. (Very scrupulous.) Another way to say it is that the person is very moral.
I'd imagine it'd come up in conversation something like:
B: {outlines some plan}
A: That's a terrible idea.
B: No it's not.
A: Sure it is. Don't you have any scruples?
B: I got scruples the size of basketballs.