When you start jumping into the 22" ranges you start approaching tractor trailer tire sizes capable of more weight because they have more plies and the result is more psi to support that. Not that they can't build that into smaller diameters. They choose not to.
If the rim size is the same, then the aspect ratio conviction can be true and the sidewall flexes more. If you're comparing width, I don't think that necessarily affects load capacity without taking other factors into count such as air pressure and number of plies. A smaller width could introduce more sidewall flex because it bears more force on a smaller tread width. We can go into laboring detail on those physics for an eon and it's just not in me to do that anymore.
I think moving to 22 is a good, given the number of plies and their make up supports more load capacity (e.g. steel v. polyester v. fiberglass, etc)
Here's a lot on minutia on it for your entertainment