I don't think you have given me enough background on the scenario to form an opinion.If the child doesn't have physical factors that lend to obesity( slow metabolism, heredity, thyroid issues etc...) I think that a parent might contribute to a child weight problem through less than stellar parenting skills. Forcing a child to eat when they aren't hungry, or feeding them an unhealthy diet and not providing the opportunity for a kid to get out and play or get kiddy-cise would certainly contribute to that but not fall under MY classification for neglect/abuse. There is nothing my son would rather do than playstation3 and surfing the web and would like to consume candy, soda ,chips and snack cakes all day. I know it is my job to feed him healthy food, monitor his snack intake and make him GO THE FUCK OUTSIDE AND PLAY!!!! Raising a child alone is not easy and sometimes that balance is not easy to find..
However if we are talking about somebody locking their child in the house in front of the tv with a box of twinkies and a case of mountain dew so they will placate themselves while the adult leaves to go play video poker then that would fall under neglect to me...
I do know this though.. God has a way of sorting these things out. In his time all things come to light and all problems are solved according to his plan