They probably can't fire him for his weight, though the job really does require someone to be fit. I worked for the post office very briefly, and I mean briefly, like two weeks on the job. I quit but you probably don't want to hear how the whole hiring process works or how tough it can be to get a full time position
I was surprised at how the packages were handled at the facility I worked at though. I was in Arizona and was a part-time mail carrier, and while I had to get my mail in order (some was machine pre-sorted in advance), the packages were handled by a few other employees. They weren't carriers, they actually are the people who worked the counter when the post office opened but early in the morning they sorted packages. They had to place them in large bins, there was one for each route. I say place but what I should say is throw. They literally throw the packages across the room as they have a couple long rows of bins and just know which one goes to each route. Sometimes they miss and the package slides across the floor. That's a good way to break things so make sure you pack stuff tight. I couldn't say if every office works like this, that was just my experience.
However, that doesn't explain packages getting smashed entirely, though I guess if it's at the bottom of the bin a heavy one could land on top of it. I suspect they don't really throw the heavy ones, probably don't have the strength for that
I'm not entirely sure how you go about filing a complaint. You could try talking to the mail carrier but then he'd know who is complaining if you need to go beyond him. For other issues though, don't bother venting on a carrier; I had to take some of that and I was just a back up, meaning I had no regular route and couldn't exactly fix reoccurring problems, I just went where I was needed. My office did have two managers so you could try calling and asking for a manager, though I suspect they might defend their employee. The other option is getting in contact with the local postmaster. It's probably not that easy to get their attention as they oversee many offices and are generally very busy. They must have a primary office though, probably at the HQ for the region. I had to do all of my training in Phoenix even though I was working in a town on the outskirts about 45 minutes away. If you live near a major city that's likely where they'll have the main facility.
