Help! Exchange of wedding gift from Bride & Groom

I've heard that it's traditional to exchange wedding gifts between the bride and groom. Who else has heard the same thing?

And, what ideas can you give for my gift to my groom. I already bought him an expensive watch as an engagement gift a few months ago. After we got my engagement ring. (Yes, I picked it out with him and it's a lovely princess cut diamond solitaire.)

I don't mind getting him another gift if that's customary but I'm not sure what to get. I'm kind of on a budget now since we are sharing wedding costs. Any ideas?

And, also should I insist that he should get me a gift as well. Maybe put a price cap on it. This is all a bit awkward.

He believes our wedding gift is each other. And, I think so too for the most part. But who doesn't like another gift.