I most recently flew domestically in the USA back in June, in and out of Tampa Florida. The airline was United and their affiliates (Continental etc.)
I recall that the checked-in luggage is limited to 2 pieces, each of 50 lbs. I used my electronic bathroom scale to weigh each of my 2 items, and they each came to 45 lbs. One of them contained all my scuba gear, while the other contained all my clothes. So this worked out nicely.
The carry-on was limited to one relatively small piece, which needed to fit into a sizing box at the airport. You can call the airline and they will tell you the dimensional rules. Or you can go to the airport yourself and take a look at the box, which is normally over by ticketing. However the best thing is to bring the smallest bag that you have (I use a small gym bag with a shoulder strap), and keep the contents to a minimum.
My carry-on normally consists of my 2 masks, my O2 sensor (since I dive nitrox), my computer and backup timer, lights without batteries (put the batteries with your clothing in check-in), camera, film, and a book. These items are fragile and breakable, so that is why I carry them on.
The TSA people are much more courteous now than they were several years ago, at first. The must have been sent to sensitivity training in the meantime and were taught how to smile and be polite. So it is no longer like being processed into county jail anymore.