How do genetics affects obesity in children?

Only a little: Prior to 1979, pediatric overweight/obesity was at a flat rate of about 5% in the U.S. It had been at 5% since the records were first kept, beginning in the 1950's. Starting in 1980 there has been an increase every year, and we are now near 20%. So it appears that about 5% of kids will be overweight/obese and part of that is genetic. The rest is related to our lifestyle in this country.