It sounds like your grandmother and mother are likely worried about you. It sounds like you know what you're doing, but a lot of people aren't very smart/educated about weight loss.
If you're worried about it, or even if you want to assauge their worries some, talk to a doctor about it. If you're not worried about it, lose it if you want to. Like you said, you're the one that benefits.
*snugs* I know what you mean about bad family situations. Some people just truly suck.