My DD does this with my belly button and a mole on my tummy. She used to do it with a small mole on my face or my nose, but that got painful and annoying! I wish I'd put a stop to the belly button thing too. But I think most littlies like to fiddle while they're feeding, it's just that whatever's closest at hand cops it!

So I wouldn't find it weird - but I might feel sorry for you if I saw it because I so understand!