How do I figure out motor sizing when I've been winging it this whole time?

To do this from scratch you have to start with the required power output, not the motor specs. Since the load weight is known, you calculate the force being carried by the belt. That force then dictates the required torque at the pulley based on the belt's radius. But you can't just stop there because belt friction and material slippage will eat into that torque. You need to figure out the maximum load and then multiply that by the efficiency of the belt and the overall drive system to get a real-world required torque value. The math usally boils down to (load force * belt radius) divided by the number of belts, factoring in slippage. Once you have that effective torque, you factor in the service factor, which is just your margin for safety. A standard 1.25 to 1.5 factor is a safe bet for initial sizing.

I've done a few of these and the thing that saved me was calling the motor distributor and telling them exactly what the load was and how fast I needed it to move. They ran the numbers for me and picked a gearbox off the shelf. Free engineering, and I learned the process by checking their work afterward. Also worth a look in your own shop, the drives on existing conveyors have nameplates, so you can see what a similar load acutally got specced with. One thing I'd add, whatever motor you land on, make sure the start-up condition is covered. Getting a fully loaded belt moving from a standstill pulls way more current than steady running, and that's usually what stalls these things on day one, not the running torque.

One thing that'll bite you is acceleration. Sizing for steady running is only half the job, the motor also has to spin up the loaded belt from a standstill, and that startup torque can be alot higher than the running torque. On a chip conveyor I did last year the startup load was close to double the steady state, and I only caught it because the drive kept tripping on the first test run. So once you've got your running torque, add an estimate for getting the whole moving mass up to speed, then apply your service factor on top of that. Also write the calcs down properly this time. The pretending works until a drive fails and someone asks why you picked that gearbox.

One thing that helped me early on was writing down every assumption on the calc sheet itself. Belt weight, load weight, where I got the friction figure, all of it. My boss could see the thinking even when a number was rough, and honestly it made me look way more switched on than pretending I pulled it from memory. Also don't panic if your torque number comes out small, conveyor motors are usually running at a fraction of what people expect once you actually do the math.