Recreational & Family - Appropriate tire size for towing a trailer?

I have a Trek 1000c with the stock 700cm 28c tires. I just took my 1 year old son out for his first ride in the trailer this weekend. It went well, and he had a blast, so I'm looking forward to riding with him a lot more.

One thing I noticed though, even though I had the rear tire aired up to the recommended PSI, once I hooked up the trailer and got rolling, I noticed that the tire was squashing under the added load.

My question is: is 28c too thin? What size should I consider? I'm not even sure what the max size my rims/brakes will support, but i'm afraid that I'll wear the tire out or risk flats if I keep riding with it.

Thanks!

I have a friend who pulls his daughter in a trailer. He has 700x23 tires on the bike. I never noticed "squashing under the added load" when I was riding next to him.
Fatter tires often look squashed with extra weight. They're wider so they spread out more, giving the appearance of being squashed.

Dunno, on my Burley (Encore), the tongue load is almost zero. I can't imagine any extra squishing; I usually pulled it with a road bike with 23mm tires.

Yes the trailer shouldn't be any extra load at all. I've been riding a new bike w/ 32s and find I need to pump the tires up a lot more, at least weekly if not more often, than the 2.0 inch tires on my regular commuter.

I'm beginning to think that perhaps I didn't have that tire aired up correctly. I'll try another run and see if I still notice anything strange.

Our trailer adds very little weight to the bike (5 pounds?). I usually run 28's on my bike pulling the trailer and riding on packed stone rail trails. When we moved our son to a burley Piccolo tag along I had to move up (running 35's now).

I'm beginning to think that perhaps I didn't have that tire aired up correctly. I'll try another run and see if I still notice anything strange.
Also check the "tongue weight" of the trailer when it's loaded with your son and whatever else you take along. I.e. about how much force do you need to exert to lift the end that attaches to the back of your bike? As others have indicated, this is usually only a small fraction of the overall trailer plus cargo weight and therefore not much additional load is placed on the rear wheel. But it might be the case that your trailer has the load farther forward and therefore has a much larger than typical tongue weight.

For best handling it's usually recommended that the tongue weight be around 5 - 10% of the overall weight and you can usually make some adjustments in where you place the child and other gear if needed. Check with the trailer manufacturer for their recommendation if the tongue weight seems too high.

All rear tire will deflect under load. You can't chane the laws of chemistry and gravity.