We always bring stuff, packed in our bags, which we check, when we fly.
Most of what we bring is snacks, we can share with the kids, when they get hungry at the parks. Also, we have found that when we are in a longer line, and they start to fuss, a little something goes a long way in making the wait more manageable.
I put the snacks in a shoe box, small shipping box or disposable plastic containers. I also double wrap anything containing liquid in plastic. I don't use anything that I won't through out while I'm done there. I don't want to bring any more back home than I have to.
Also, I started to use a seperate bag for snacks, food, and water/juice boxes. I have an old nylon duffle bag, which is a little less than 3 feet long, with sturdy handles. What I like about using this is that it doesn't add weight to our regular luggage, and when it is empty, it rolls up into a very small space for the return trip.
Remember that new weight limit is now 50 pounds (I think it has been lowered from 60). For larger bags it is easy to reach 50 pounds, just with cloths.
SW lets you check three bagw per person. For our family of four, that is 12 bags (about twice what we need).
It is odd that they will let you check that many bags, but when we only had 3 checked bags for four people, they wanted to charge us $25 extra dollars, because our big bag was 2 pounds over.