My husband and I don't know how to approach her with this. She will say we are "fat shaming" her and then will shut us out. I really don't know what that means but I do know she will shut us out of her life for a while if we broach the subject. Her boyfriend has the same experience.
What you are experiencing is something another parent went through on here earlier in the year.
The social blogging site
Tumblr often spawns a lot of strange trends that are on the extreme end of political correctness. Through misinformation, guilt-tripping, and capitalizing on uneducated individuals looking for a place to belong online, these ideas are spread rapidly.
People who spread or follow these extreme nonsensical trends (in your case, "fat-shaming" are called "Social Justice Warriors" - people who believe they are standing up for an injustice in society that isn't actually there in the first place.
As a 22 year old talking to someone much older who doesn't understand this strange phenomenon,
I can assure you that you aren't doing anything wrong. Gaining 100+ pounds is indeed extremely unhealthy and not something to be proud of. Your daughter has simply bought into a nonsensical trend on the internet.
"Fat-shaming" is a term created by Social Justice Warriors to avoid the responsibility to actually take proper care of their body and instead victimize themselves by pretending they're discriminated against like an ethnic group.