Yes you're doing the right thing. Don't use it as a reward ever...just don't buy it.
I had a similar problem...not perhaps as severe because DD never actually got overweight but she was heading that way.
I stopped buying all crisps, cake, biscuit and snack type foods...nothing processed at all. Not even juice.
Rather than removing sugar, remove anything that isn't a whole food.
So have fruit, have meat, fish...veg and salads...do not have yogurts, biscuit bars, and cereals other than porrige oats.
Bread is ok in small amounts...not sandwiches daily.
Cheese...a little cut up...it's a protein and has fat in it but it's not a terrible food...but I treat it as part of a meal and not a snack. So if DD has a baked potato and salad then she can have a bit of grated cheese too.
Tuna is good...watch portion sizes...google amounts for a child and stick to that. Do NOT get upset when he cries he is hungry...insist that he's thirsty and needs water or offer an apple or raw carrot.
If you don't get it in check now it will get worse.