I tell people that's my superpower. I had HE with all three pregnancies, all three I threw up constantly for the first few months and yet gained weight.
With this one (due last Sunday) I couldn't even get most food near my mouth. For two weeks all I ate was one egg in the morning, about 1/4 cup plain yogurt in the afternoon, and sometimes yogurt, sometimes a small piece of meat for supper. And I threw up a lot.
Adding up the calories got me 600 - 800 a day. And yet I gained 1.5 pounds both of those weeks. And also for the next two weeks when I was able to add, of all things, pepperoni pizza to my list. And for the next few weeks when i could add peeled fruit.
Zofran made this pregnancy more bearable. I was able to stop taking it after month 5, though i have thrown up every morning this entire pregnancy. And I'm still nauseous most of the time. Sucks, doesn't it? I'm so ready for the baby to show up.
I couldn't drink tap water sometimes, have you tried sparkly water? Also,oddly for me, coke with lime over crushed ice, almost a slushy (and I am not a soda drinker!) Being hydrated helps a little bit, but getting those fluids can be impossible when you can't stomach anything.
Good luck, I feel for you!