You're probably feeding bad food, dear! Cats only go after people food with intensity if they're being malnourished from the food they eat.
Dogs that are being fed poor food eat their own poop and eat from the garbage... cats will look for human food.
Puking is NOT good. You need to feed better. What are you feeding? Malnourished cats will also need to be fed more..you feed better food, you feed less.
You need to buy a better food, that's the ONLY thing will solve it. Natural Balance Ultra Premium dry food would probably be a good food to get her pack some weight on and stop puking. Chances are, if the food you're feeding now contains corn, or soy, it's probably a reaction to that. You need to avoid foods with corn, and soy especially. Byproducts(poultry, meat byproducts or "meat meal")..you need to avoid all of those. You could also feed Innova's Healthwise - Chicken and Rice. It's got rice, which is a grain, and isn't ideal(cats and dogs shouldn't be eating grains). That shouldn't upset her tummy, either. But her puking should stop once you change her food.
That happened to one of our cats...not to that intensity...but she would puke several times a week. One night, several months ago, she started crying(she cries before she's about to puke - it's heart-wrenching, but that's how we know to prepare). I tried to hold her steady, but she was puking so violently I was afraid I'd hurt her if I kept a grip on her. I took some Fancy Feast my fiance's mom had stocked up on for emergencies(Fancy Feast is not a good food, but it worked). And I gave it to her to fill her belly. She didn't puke it out, thankfully. But I changed them to a better food when I could. And the reason she puked was because we were feeding on what my fiance's mom feeds the rest of the cats - Purina Cat Chow. Bad food. And it's why she was vomiting. She hasn't puked since that day.