cat diagnosed with over active thyroid

my cat who was a very fat cat is now on thyroid meds

Her hunger has increased like crazy but i think she is getting thinner (which is good)

Do these meds put cats back in shape?

Yes, the medication should make the thyroid operate normally.
BUT it can sometimes take several adjustments to the exact doseage of the medication before the proper dose is figured out.
I would suggest you call your vet with your concerns; it is dangerous for any cat, regardless of the reason, to loose weight too fast, particularly, an overweight cat (as ironic/contrary as that may seem).

The vet is happy about it he knows how fat shewas and said she can get diabtes easy like that

My other vet also said the samething shes wayy to fat and that she must reduce weight asap but anytime we tried she would get UTI from food change

Now she has UTI plus thyroid BUt the vet said shes a really healthy looking cat and kidney everything is fine and she has a thick nice coat for a cat her age, I was thinking its probably wet food?

But i cant find anything on thyroid and weight gain all i see is thyroid and weight loss for cats? She was fat on no pills and getthing thin on pills?

I have to give her this for life they said.