Fat parent have fat kids, and lazy parents have fat lazy kids. It's a crazy combination of nature and nurture perhaps.
There may be a genetic predisposition toward being fat, but you don't have to be that fat person, if you're clever and eat and exercise, you can beat that predisposition, in spite of your genes.
I think part of the whole problem these days may be unresolved guilt feelings.
A lot of parents are doing too many things, and not giving their children enough time, so they pander to their child's every want, so the child is 'happy'. The thing most children want most from their parents is love and attention.
If you begin as you hope to continue, you should be OK. I have to admit though, that I found it difficult when my son was small, and underweight, I fed him whatever I could get into him because I was terrified he was starving. I was breastfeeding him, visiting the baby nurse, and slowly going mad from post natal depression (without realising it). I’m over it now, and all is well, but it took a while.
Now, sixteen years later, my son is short for his age, compared to a lot of other students in his year level. But I'm short, my husband is not tall, my parents and his are/were all short. I think that, back when he was a baby, if the nurse had really thought about genetics, we could have all realised this baby was never going to be big, and we could have relaxed and enjoyed it all so much more.
I feed my son and my husband and myself good nutritional food, with the occasional yummy treat. We exercise a little (far too little on my part) and we are all working at getting to our healthiest state we can. It won’t happen overnight, but, with focus and work, it will happen.