Sounds like it definitely could be reflux, or something GI related. My 9 year old was diagnosed with reflux after his dentist found 8 cavities and a spot on the back of a front adult tooth last year. After we asked him about it, he definitely reported feeling acid come up into his throat and mouth, but didn't realize it didn't happen to everyone. We saw both our pediatrician and GI. DS has never been underweight though and doesn't have other GI problems so our pedi handles it now. We've seen an improvement after starting a PPI and he says he notices if we miss a day or two.
Mixed with the history of being underweight, I think it's not out of the realm of possibility for sure.
Mom to Two Wild and Crazy Boys and One Sweet Baby Girl