Granted, you only wanted to show him love and give him everything to enrich his life...but if you LOOK at Billy, you see the results of a parent taking the EASY way out of parenting situations...it's easiest to put a plate-full of "love" under a child's nose and allow the TV to be a child's babysitter... This Mother loves her son, but just imagine if she had rewarded Billy equally with experiences, activity or anything other than food and idle behavior?  ...Billy would have a half-ton of knowledge in his brain...love in his heart....and he would literally have his weight in self confidence!
It's not much different than a Mother showing her "love" to her son by giving him Drugs...and then morning his death of an over-dose... 
Mom needs more therapy than Billy...she speaks to him like he is a baby...and I have no doubt that she will be responsible, post-surgery, for his undoing any weight loss that occurs during his post-op phase.  It's tough to see the result of mis-guided love, but it's also very sad when it's to a point where the one who is "loved" is so close to death!
I'm sorry...it sounds very odd...but I view this as bordering on Child Abuse