L.H.
As a person who struggles with weight and has since the age of 9 I can understand the hurt feelings. I also understand your kid is 6. I think a hand written apology is great. I agree with the empathy point others have made below.
I've told my mom countless times that I feel like obesity is still a thing people feel ok about being very critical to others about. It's not ok but our society thinks so. My son carries extra weight. His pediatrician got all over us about how he should not drink sugary drinks and get more exercise blah blah blah. Guess what??? He drinks water constantly, thinks soft drinks are horrible and never drinks but 1 6oz glass of milk in the morning and then water the rest of the day (his preference). He is active, he's allowed 30 mins of screen time daily. Every accusation made he was not guilty of and when my son tried to tell him he didn't do those things he looked at him like he was lying. Guess what? As soon as we left the office my son broke out in tears and sobbed the whole way home. He has men in his family who are 6'5" and weigh over 200 lbs. They are giants compared to my side. I comforted my son and made another appt with his ped and explained to him how much effect his words had.
We all have things we struggle with. We are still conditioning our kids that being fat is a horrible thing. You know what? I'd rather be around a heavy kid with a great heart than a beautiful one with a mean spirit. One if my favorite sayings is yes I'm fat but you're mean and I can diet.
If your child did that to mine I would tell my kid I am fat the child is pointing out the obvious which is so silly. It's something I know because I carry it all the time. Please don't let what one person says ruin your day. I'm sure he didn't mean to hurt you but if he says it again you tell him it's hurtful and to stop.
The kid is 6. You can teach your child and you're now aware of the issue. Do not let this moment define the child.
Blessings!
L.