I don't think weight is that important, but I wonder if people with certain body shapes can never swim well?
Some may have disadvantages, but I think you can overcome this by trying to minimize them and by focusing on strengths. For instance, I naturally suck at UW dolphin kicking due to my shape and proportions, yet I can naturally flutter kick quite well. I just spend much more time training the SDK then flutter kicking. I also surface early from starts before my momentum falls too much because I am faster on the surface
I'm definitely overweight. In my prime I was 130 pounds and only 5'4" heavy for a swimmer. Now, I over 200. Trying to swim again to control some weight gain and pre-diabetes.
I have lost about 50 pounds over the past several months and have definitely noticed changes in my swimming that seem to be more related to my weight than my increased endurance, speed, etc. I used to be so buoyant that when I used an adult sized pull buoy for pull sets I was too buoyant and would have difficulty controlling my rotation. i used to be able to easily float vertically without doing much in the way of treading. I've lost some buoyancy as I've lost the weight. I still float fairly easily, but I don't pop to the surface quite as quickly when I push off the wall and I have to tread a little to stay vertical. Luckily since I lost the weight in a slow 2 pounds per week way, these are things my body has adjusted to without me noticing along the way. I only notice them when I think about what swimming and floating used to be like.
I agree with the other comments about sometimes people who are leaner and/or more muscly having more difficulty that people who are rounder or overweight. Being naturally buoyant can provide some comfort while learning to swim that "sinkers" don't really have.
I've always been a big guy, been swimming since I was 6, quit competitive swimming at 18 with university around the corner. Even at 6'3 and 280 pounds now, I swim just fine. Would I be a better swimmer if I lost more weight? Obviously, so that's what I'm doing and on the right track again.
I am more easily out of breath and my speed has definitely suffered as opposed to when I was younger, but my technique is still good and while I am definitely overweight, I'm more on the athletic side of being overweight (if there's a good side to it at all).
Short: get in the pool, don't fret over your weight. There's only 1 way to work on it and that is to start working out.
Yes anyone can learn to swim. I taught a war vet how to swim starting from how to breathe up to swimming 800 yards . He is 6'2" 265. He learned and practiced even week and he and I are proud of his efforts. He is now certified as an open water scuba swimmer!!