Last week I spent the night in JFK and was surprised at the number of people there for the night. I was originally told I could not check my bags (changed airlines) but a Delta employee took pity on my and allowed me to check my bags very early so that I could go through security to where there was a more comfortable seating area. The reason I mention this is she told me in order to check my bags, she would have to bring them over to AeroMexico where they were equipped to accept bags overnight. Apparently some of the international carriers have flights arriving at odd hours and can switch bags to an American carrier bypassing the regular rules. If you get pushback on checking your bags through and having to recheck them early, there may be some helpful advice/terms in there.