I had an obese uncle (about 500 lbs) growing up - he was my favorite. A person who is obese understands that they are overweight, I think. Anyway, it was common knowledge that my uncle was really hard on dining room chairs - they just aren't designed to take so much weight, and my grandma complained for years about all the chairs getting wobbly until they came to the decision that my uncle would always sit in one chair, so he was only wearing out one chair - and keep in mind he was there every day so it took a long time to wear them down - maybe your furniture is more resiliant than you realize! So everyone had a "my uncles name" chair at their house. He was not offended when someone asked him to "sit in this one over here", we all had a way of faulting the chairs more than my uncle, who was fabulously funny and great with kids and all around a wonderful person. In the end, it was much better to have him there and deal with wobbly chairs than get worked up about stuff, but of course I guess that is family which is different than a money making venture.
I'm sorry you were bullied as a child, and I think your desire to show kindness and empathy is really good. But there is a difference between bullying someone and being frank. I think if you show that you are willing to accomodate and work through the problems with them, and if you show that you are really delighted to get to know them as people, they will understand the issue - surely after all these are issues they face every day in their own lives? A person does not become 500 pounds over night.
So what specific issues are you worried about? If you have a new mattress, for instance, it is likely still under warranty. If one night of sleeping under these guests does in the mattress, the mattress is probably warrantied against a certain amount of compression within say 5 years? Sure it would be a pain to get it replaced and deal with the warranty, but the mattress is something that is probably relatively easy to fix without cost in that scenario. If it is the frame of the bed you are concerned about, I would address that one outright: "Hey, yall I have to be honest I have had all kinds of guests stay here and this bed frame sometimes seems wobbly even with my cousin - he's a linebacker and he complains about it's gonna break on him. I just worry with both of you on this bed it might give out and I don't want that to happen to you. Would you mind if I just set the bed off the frame that way we don't have to worry about it?" If you are worried about them passing through the shower doors, well, a night without bathing won't kill someone and that would be obvious on their own inspection. I looked at your pictures, so it isn't as if the fact you have shower doors is some kind of surprise. They must have known that at booking. A toilet coming unseated would cost something to correct, and maybe that is something you could discuss with Air if it indeed becomes a problem, but maybe it won't be a problem at all.
Hope everything works out and you don't have anything to resolve with Air.