It’s a bit more nuanced. Your average modern garage door isn’t going to have much weight difference. The difference will mostly be related to hight and width but that weight is offset by the spring. A properly installed 7x8 door should open with a similar effort as a 7x16. One could argue that there maybe be a little more mass to get the door movement started but over all it should be the same amount of effort. Higher hp units generally aren’t required unless specified by the door manufacturer due to something unique about it. Just like why would you buy a 2 hp garbage disposal when a 1/4 works about the same in 95% off applications. Sure a higher hp opener will do better and last longer on a larger door but the only real difference it might encounter is the starting inertia.

Don’t believe me? Pop the string lock on two garage doors, a single and a double and feel the difference it takes to open both. But I’m referring to modern aluminum doors, things can get a little strange with old wooden doors etc.

I got an insulated garage door for free, it was a 16x16, older style and heavier. I installed it on my equipment storage shed so tractors could get in and out. The springs were huuuuuuuge, two on either side about 7ft each. Guess what I opened it with? A 1/2 horse residential opener I got off Craigslist used/broken for free. Fixed it (bad sensor wire) and it worked for years until I moved. You could tell it was pissed of initially but once the door started moving you could hear it idle.

The other consideration is duty cycle. When it is 90 outside, you leave the door open or shut until you are done. Open and close it 6-8 times in close succession and it goes into overheat shutdown and flashes the lights with that error code until it cools. If I used a 2hp opener it would be able to open and close many more times before it’s over heats. You’re going to say yeah it is overheating because it’s working harder. Well… more nuanced. It’s having to run for a longer time between open and close, 16 ft door so longer run times. And yeah there is still mass in the door that takes effort to get started but once in motion it’s not much different then a small door. I would argue if you looked at a current meter that it would be very similar other then the initial start.

That 16x16 door was so well balanced I could open it and close it with my pinky. It have it sit 1/2 open without the garage opener all day long and before I installed the opener my children (4-7) at the time would open it by them selves, lift and jump push to get it to go all the way up so they could pull out the atv or power wheels.

I also had on the same building a 10x10 same story 1/2 hp opener no problem, that door was brand new and a lot lighter though still two decent sized springs.