New cat won't eat.

Very good. Try giving her scheduled meals.
How old is she? How many times and what's the amount you are giving her?
Does she eat together with the other cat or does she eat at separate room?

Zelskid said:

 
Feliway plug ins and sprays?

Click to expand...

Yes. They give off the feel good pheromones that cats naturally have and work as a calming agent for some cats. They can be found at big box pet stores but Amazon has the best prices I have found

Happy

My Katy is a fussy eater also.  I brought her home from a shelter last December.  I had the hardest time getting her interested in eating anything other than the dry Hill's Science  food that was fed to her at the shelter.  I weaned her off the Hills with dry Kitten Chow and canned Sheba or Fancy Feast.  I fed her either a can of Sheba or Fancy Feast wet brands  twice daily, with a bowl of Kitten Chow (dry) always at hand.  It has done the trick.  I was so used to feeding ferals who will eat everything is site that when I adopted Katy, I thought something was wrong with her because she does not scarf down the food like the ferals do.  I needed to remember that she does not need to eat as if this were going to be her last meal.  I also needed to remember that just like people, all cats are different.  As long as they are healthy and of course happy, just enjoy the ride!!

I am too aggressive with my affection

But with leaving so much food out Honey is getting fatter

Zelskid said:

 
But with leaving so much food out Honey is getting fatter

Click to expand...

Ok so you have Lola who is not a good eater right now and Honey who is eating her own food and Lola's as well? 

Yeah, that can be tough. You may have to separate them for now just until Lola becomes comfortable and starts eating normally. At least feed them separately and when Lola leaves food, remove it so Honey cannot get it and then offer it to Lola if she seems to be looking for food. It's more work for you but it will help insure that Lola gets her own meals. 

They never get near each

Lola loves her cat tower and Honey never goes near it

Is finally  eating..Honey tries to take her food. It doesn't  take much to fill her tummy.

That is good to hear that Lola is eating now. Does Honey eat at the same time as Lola?

It's good that Lola and Honey are tolerating each other.
Maybe the tuna would be tempting for her.