I have a ten years old cat that I used to fed twice a day but now it asks for food every time she sees me. I started to feed her three times a day and she has grown considerably fat.
Is this good for her?
Smaller meals more frequently are better for your cat than fewer larger meals.
I wouldn't feed it "as much as it wants" unless it is keeping a good stable weight.
Try to feed it so that it maintains a stable weight and is not too skinny or too fat.
If she is too fat (as you suggest) trim her down, you can still feed her multiple times a day, just cut the portions down. Don't do a crash diet, feed her so she slowly looses the weight.
You could probably consult your vet by phone for free in regards to what an ideal weight is for your cat.
The answers provided so far are quite good already: overweight is dangerous for the cat's health and frequent, smaller meals are better than one/two big meals.
So your solution is to reduce the quantity of each meal, possibly keeping two or three meals a day.
Stimulate your cat's hunting and chasing instinct
What I would like to add is that it is normal for cats to be on the hunt all day long. The innate instinct of cats is to hunt their preys, which are usually rather small. The way we feed our cats usually goes against their predatory instinct and cats can become bored about food or feel uncomfortable not having a possibility to access food (reference).
Additionally hunting or "playing for food" is an excellent mental stimulation that will benefit the cat mentally and physically.
So I would recommend giving the cat access to some kind of food puzzle. A few well known options are (see links and pictures):
As you are now feeding your cat "the usual way", you could proceed step by step: give your cat half of his meal in a bowl, when he's done put the other half in one of the toy and given him access to the toy. If he likes it, you can then just fill the toy twice a day.
I assumed that you feed your cat dry food, the question "Should my cat be allowed some wet food every day?" has excellent answers about wet food.
One good solution would be to give your cat wet food once a day, and free access to a toy with dry food during the day. If you control the quality of the food and its quantity this is not incompatible with preventing the cat to gain weight.
You can also have a look at this paper: Environmental enrichment for indoor cats which is a detailed discussion (problems and possible solutions) in reference to the AAFP (American Association of Feline Practitioners) position statement on Environmental enrichment for indoor cats. Both cover cats' feeding issues.
Catit feeding maze
If the term you're using is considerably fat then the short answer your question is: no, it's the opposite of good. In fact, it's very bad for her. Here's the essential risks of obesity in cats:
Not sure if your cat is obese, that requires some measurements that a vet can perform for you, but if you're seeing the change, chances are good that it will get worse. So, what can you do? Well, food choices and your resistance to her demands are going to matter. Some things to do:
Now, you should still take her to the vet for a consultation and check-up.
As supplementary information to the other answers, a veterinarian will be able to give you advice specifically for your cats needs, whether it needs exercise, healthier food, or different feeding times, similar to my answer for How much should I feed my puppy?
A vet will also use a weight chart to determine the condition of your cat, as shown below, which can help find a course of action specific to your animal.
More information can be found at PetObesityPrevention.org
What I remember from the cats I had, they like the canned (wet) food, not so much the hard dry food. Give them limited wet food. I don't know what a normal cat would need, but that won't be too difficult to find out.
I always had a tray with dry food in the kitchen and they could eat as much as they wanted. So they always had sufficient food available, and if they were really hungry, they could eat as much as they needed. Most of the time the tray was filled and they didn't eat much of it.
Read the book Don't shoot the dog by Karen Pryor. It's a fun book about behavior, and how you can change it by using positive and negative reinforcement. Spoiler: negative reinforcement doesn't work - especially with cats, but... positive reinforcement does work really good. This book is mostly about dogs, but you will find some really nice insights in your own behavior, and it might inspire you to handle your cat differently.
Becomming too fat is rather unhealthy for cats, especially if they have little excercise. But now that your cat is used to getting fed three times per day, she might become a little bit annoying if you switch back to two meals. However, you can feed smaller portions, i.e. not give her the whole pack at once. Cat food can be stored in the fridge for several hours, and if you let it warm up a little bit before feeding, your cat may not notice.