When I go to the Caribbean I check the dive bag (containing diveskin, booties, fins, weight belt sans weights). I carry on mask, snorkel, and flashlight: the mask is a nice one and the piece I'd most hate to lose; the snorkel I don't want to get cracked when the bag is tossed around. As for the torch, I'm concerned the batteries will cause it to get my bags pulled, whereas it is easy to demonstrate/disassemble/explain in a carry-on. I do not own a BCD.
My baggage actually got lost on the way to my cert dive. I was fortunate that I was able to borrow fins, rent a BC with an integrated weight belt, and that the water was warm enough around Grand Cayman not to require a wetsuit. When I went to Cairns I didn't bring a thing; rentals were all-inclusive but more importantly I would only be diving 3 days out of 20 and didn't want any of it taking up space in my backpack, risking theft, loss, or damage.