Sounds like your best bet
http://m.military.com/join-armed-forces/coast-guard-weight-rules.html
So according to that you’re like 5’0 – 5’3? I’m guessing that frame size code is wrist circumference. It just doesn’t make sense unless you’re that short with really thin wrists, which would make it hugely surprising that you got as heavy as you are to begin with.
Aside from arguing with them more, or trying to lose the weight, you could try for another branch, dunno how much more lenient they’ll be though.