My budgie is very clingy/hates being inside his cage

I've had him for almost 3 weeks now and he has been to the vet 4 times already since I was getting him treated for a bacterial infection and yeast infection. He recently tested negative for chlamydia so my vet said he had a clean bill of health now.

However, he has become very clingy and hates to be inside his cage. Whenever he's left in his cage he will fly around inside his cage trying to get my attention, begging to come out.

I am worried as he is underweight and he doesn't seem to be eating enough as he spends all his energy begging to come out of his cage.

Any tips/advice?

Thanks!