A lack of family support is probably one of the most common problems that people on any diet find. The reasons for that are many and complicated but one of the most common is: We as humans seem to have a natural resistance to change. Change makes us feel uncomfortable and when that change is going on in the lives of people closest to us, the level of discomfort is often even higher.
Rather than go into the whys and wherefores of this, I think it maybe more fruitful just to cover actions that we can take when we're faced with this type of situation. Without making a big song and dance about it , we need to assure those around us that we are doing what we're doing in order to have a better quality and longer life so that you can spend more quality time with them; whether that's your children, your other half or any other person who cares for you in any meaningful way. Offering that type of assurance will short-circuit many of the fears that those closest to us may have about the consequences of our changing.
I'll give you an extreme example; a story that was related to me from a source I know I can trust was concerning a middle aged couple. He has had a health scare and decided that the best thing he could do for himself and everybody he cared about was to put his health in order. So after getting some good advice, he started on a low carb diet and increased his amount of daily exercise. Ten weeks after starting his new healthy lifestyle, he was looking, one has to say, like a new man to the point that his wife's friends started to comment to her how good he was looking. Initially, she just accepted this with pride and was slightly flattered that they noticed but unfortunately an innocent comment from one of her friends, which I think honestly was misconstrued, as they said "Gosh! He looks like a new man! Perhaps he's looking for a new woman". While initially, this was received with a highly amused laugh started to prey on her mind to the point that she became concerned that her husband of twenty-something years was planning to leave her for somebody else. It took quite a bit of assurance from the husband for her to understand that the only new woman he would like in his life is the one he has always had but maybe just a bit fitter than she was now.
Fortunately the outcome from this little tale was a happy one. She couldn't deny how much better her husband was, how much more funny he had become to be with, having more energy, more stamina and the greater inclination to do the same things that they used to do when they we're younger and fitter. She was as encouraged to follow something very similar and the last I heard, they were still together but living interesting and active lives.
As far as costs go, well, mdanziger has said , whilst the short term cost may seem a little bit higher than eating garbage, the long term gains of better health, fewer visits to the doctors seems a much more sound investment to me.
Hope that helps,
Mark