Pediatrician told me to feed my son less often

I only feed him when he shows hunger cues, I don’t push it to 2-3 hours because I know when my baby is hungry and he knows when he’s hungry too. He’s 2 months now and weighs 13 pounds, he was born 6 pounds and was 8 pounds at his 2 week appointment so she said he put on weight too fast and to try to sooth him other ways and only feed him every 2-3 hours. He eats about every 1- 1 1/2 hours and I’m not going to feed my son less honestly, he doesn’t even eat if he’s not hungry. I don’t want him to get unhealthy fat or anything but I’m not going to starve him. I had thawed a bag of milk for him and saw fatty oil in it. Is it my milk that’s too fatty and making him gain weight? 🥺