Good morning, I'm Dr. Sara. I'm a licensed veterinarian who works exclusively with cats and dogs. I'm sorry to hear that Willow hasn't been feeling well!
When I have young to middle aged cats who are vomiting and not eating, the one thing I want to rule out as quickly as possible is a foreign body obstruction. This is where the kitty has eaten an object that is obstructing the GI tract - often strings, ribbons, or other fabric items are the culprits, although vets have seen a wide variety of objects get swallowed! The reason I want to check for this as quickly as possible is that if they've got a GI obstruction, they're going to need surgery to fix it.
Other potential reasons for a young cat to be vomiting is an infectious disease (think stomach flu), pancreatitis, or other dietary indiscretion (I ate something that didn't agree with me). In those cases, some symptomatic care at the vets may get her through just fine. Pancreatitis can be a bit more tricky to diagnose and treat - it has a variable severity ranging from mild to life threatening.
Another thing I'm concerned about with obese kitties is a disease called hepatic lipidosis. If a chunky kitty goes a few days without eating, they can actually go into liver failure. The simplest way to explain it is that when they don't eat, they liberate fat from their bodies to metabolize for energy, but the fat accumulates in the liver and can cause significant liver damage and failure if not treated.
For all of these reasons, I would suggest that you call your vet today - also especially because it's Friday and I don't want you to be stuck over the weekend with a sick kitty that you've got to take to the ER. After a physical exam, your vet may likely feel it's a passing stomach bug and administer some anti-nausea medication. However, if there's more to it, she can get the testing and treatment that she needs :)
Please let me know what other questions I can answer for you!