OP,
It must be very hard when your own parents act in such a way. 
If this has been a constant since your teens, I expect, no matter how assertive you are in other areas of your life, every criticism takes you right back to feeling vulnerable/ hurt/ angry at previous unfair treatment?
Lack of recognition on successful completion of a tough degree a case in point.
(But well done from an anonymous MNer, FWIW 
).
I'm guessing the criticism and rudeness is also not confined to your weight per se, more that it's (very understandably) a sensitive area for you, and thus an effective control tool for someone emotionally abusive to hone in on.
I've witnessed a very similar dynamic with close friend: her father is weirdly fixated about everyone's weight (incl. his own), but criticises hers constantly whenever she disagrees about anything, no matter how unrelated.
Her mother has been conditioned to agree (always claiming it's for my friend's own good to be told/ concerns about her health etc...bollocks is it; friend runs half marathons!), friend is terribly upset, reduces contact, is told is being oversensitive, feels guilty as kids miss DGPs, relents, things improve until the next time...
I'd be tempted to answer any weight comment whatsoever from them with "Ironically, I only resort to comfort eating when my self-esteem takes a bashing and I'm made to feel judged".
But I realise that type of person you describe rarely acknowledges their behaviour is ever at fault.
Are your kids of an age to be influenced by such attitudes?
i.e. are relationships between them ever likely to reach a stage of weekly hour-long FaceTime/ Skype sessions and stays with you when in UK?
(Very different scenarios between, say, a perceptive 7yr old regularly given the message from Gpa & Gma that only being deemed thin enough by them gets approval, and who picks up on the way Gma acts differently whenever Gpa's around, compared with a 2 hr meet-up twice a year, a couple of quick phone calls between times, and Mummy and/ or Daddy calling out any hurtful comments, each and every time).
Are there really enough positives to warrant strengthening Grandparent/ Grandchild relationships, or is it far more out of guilt (they're also perhaps elderly?) that your kids would feel hard done by and blame you, if communication is only kept minimal?
None of us would find it easy, I'm sure.
Hope you manage to work out the best solution for you and your DC.