kitten plays until panting/how underweight is she?

Our kitten was born June 16, and was bottlefed as soon as she was 1 week old because the mother left. Here is my first question:

The cat was taken to the vet recently for her scheduled checkup and shots/deworming medicine, etc. She weighed in at just over 3 lbs. I told the vet she didn't seem to be growing as fast as our other kitten did, and she looks to be about the size of a kitten that is around 9 weeks old. He said she is definitely a little small/light for her age. What is average weight for a kitten her age? She was born June 16, so she's 3.5 months old, or about 15-16 weeks old, and just over 3 lbs.
Keep in mind the vet has said nothing about her seeming unhealthy. She loves to play, prefers to sleep cradled in my arm(s) while I'm sitting down, and I often wake up in the morning with her either sleeping on my chest/stomach or cuddled up under my chin next to my head. She plays with our other cat constantly and seems very healthy. I'm just wondering how small she is in comparison to most kittens her age.

For question #2: I have a common toy that has a string w/ a feather on the end of it. Both cats love to chase it, but they will both chase it until they're panting they're so tired, and still they'll continue to play. Is this common? Is it best to immediately stop playing with the cats (especially the underweight kitten, even though she is a perfectly normal kitten other than her size) when they're panting? They will still want to chase the toy and I'm just concerned that the little kitten would be more likely to have something happen if she's overexercised, like a heart problem or something along those lines from too much strain on her from all the running/climbing.

Thanks in advance everyone. Thanks to everyone on this forum the kitten made it and I learned how to properly take care of her when the mother ran off. I'll have to dig up some pictures for everyone to see how beautiful she is.

edit: Some pictures from when she was born up until maybe one month ago:

I am not sure about the weight/size thing. Maybe she is just a small cat?

As far as the excersize is concerned, when the cats are panting, i think thats a sign that they've had enough.

Are you feeding dry food? Cats who eat mostly dry food are chronically dehydrated, even if they seem to be fine. They need to ingest water with their food (canned food) in order to maintain an optimal water balance.

Originally Posted by TrixtersMomma

I am not sure about the weight/size thing. Maybe she is just a small cat?

As far as the excersize is concerned, when the cats are panting, i think thats a sign that they've had enough.

Are you feeding dry food? Cats who eat mostly dry food are chronically dehydrated, even if they seem to be fine. They need to ingest water with their food (canned food) in order to maintain an optimal water balance.

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I'm sure she's not tiny to the point of it being a serious problem. I'm assuming she's a small cat because she was bottlefed. While she still got nutrition she needed to grow up, I'm sure having her mother there would have helped her grow to be more normal size. I guess I'm just curious to know average size of a 3.5 month old cat. She doesn't seem to be growing nearly as fast as our other kitten did.
My boss has 4 cats, one of which is a few years old and probably only about 5 lbs, but perfectly healthy, so I'm not really that worried, just curious.
I'd never heard that dry food was bad if that's the cat's whole diet. We started with formula for her, then moved onto canned wet food, then dry food when she seemed ready to eat it. There is always fresh water in multiple places in our apartment for the cats, so I didn't know they needed more water than what they get. Thanks for the info.

Originally Posted by zookeeper

I'm sure she's not tiny to the point of it being a serious problem. I'm assuming she's a small cat because she was bottlefed. While she still got nutrition she needed to grow up, I'm sure having her mother there would have helped her grow to be more normal size. I guess I'm just curious to know average size of a 3.5 month old cat. She doesn't seem to be growing nearly as fast as our other kitten did.
My boss has 4 cats, one of which is a few years old and probably only about 5 lbs, but perfectly healthy, so I'm not really that worried, just curious.
I'd never heard that dry food was bad if that's the cat's whole diet. We started with formula for her, then moved onto canned wet food, then dry food when she seemed ready to eat it. There is always fresh water in multiple places in our apartment for the cats, so I didn't know they needed more water than what they get. Thanks for the info.

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My cat also used to play until he panted...the vet said there wasn't anything wrong with him..he was just an intense player.

Katie