Could my friends kitten be sick?

Okay so me and my friend adopted 2 kittens from different litters at our local spca, they were both 6 weeks weeks old and of similar age. Now just to avoid future confusion my kitten is Nidalee and his kitten is Gypsy, my experience with cats is extremely limited i used to think i wasn't a cat person and recently discovered that i love cats so my experience is limited to what I've read on the internet and my personal experience with my kitten who is only 16 weeks old.Now he told me that Gypsy wasn't growing and i assumed he just meant not as quickly as he thought she would, but i went to his house when she was 13 weeks old and I couldnt believe my eyes she legit seemed like she was still a kitten,So we weighed her and she weighed 590G (1.3 pounds) keeping in mind that she is overweight, her fur also didn't seem as soft and smooth as Nidalee's but like she was still a kitten growing her coat, she wasn't cleaning herself well either, when i got there she had some gunk on her face and when i left 23 hours later she still hadnt cleaned her face, In comparison(and this truely is the only thing i can compare with) Nidalee was 1.4kg (3 pounds) and was slightly underweight, her coat is soft and thick and she never has a dirty spot on her body. Gypsy also eats alot, like alot she eats like atleast 3/4 of her body size in food every day, and my friend says she's also started not using her litterbox anymore. I'll post some pics in a bit, they want to take her to the vet this week but are scared that they might discover that she has some awful sickness. Any help is appreciated!

Edit: i forgot to include that she doesn't really run around and isn't very interested in playing a game.

Edit2: added photos in comments

I think that your friend's kitten absolutely should go to the vet. Has it been to the vet since he got it? If for nothing else than for vaccinations, deworming, etc?

No the spca vaccinates them and deworms them

Maura Larling said:

No the spca vaccinates them and deworms them

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There are some vaccines they shouldn't have before 8 weeks, if not all (so please double check on that). Plus distemper is supposed to be a series of shots over a period of several weeks. At 6 weeks old, there's no way they could have had all of the vaccinations. So please do check on that.

But back to your post, it sounds like your friend's kitty is pretty sick. Did you say it looks overweight at just over 1 lb? Kittens should be playful and full of energy, not lethargic.

No it is 3 rounds of shots given over some time i just wasnt being very descriptive i think they gave us a couple when she was 6 weeks,13 weeks and then 20 weeks not sure if there's another round of shots after that, im trying to upload the picture so you can see shes pretty round

Looks like it could be sick and might need a referral to a board certified dermatologist.

Oh goodness, what a cutie - that little green bow, so precious!

I think Nidalee needs a regular vet, not a dermatologist. The eating like crazy, low weight, low energy... just doesn't add up to good things at all. Could be as simple as worms or as serious as FIP. But you don't really want to chance it either way. If it is something horrible, it's better to know, as sad as it may be. But I'll be hoping it's not so serious.

He is so precious!  Omg.

I'd definitely take the little kitten to the vet.  There may be something treatable, but you won't know unless you take him.  Let us know how things go!

Edited:

I just reread your original post more thoroughly.  I missed this before.  If the kitten is not using the litter box and has no energy, is not cleaning itself, she needs to be seen by the vet TODAY.  If they can't see her, then take her to the Emergency Vet.  Something is definitely wrong and it sound like the little one is declining fast.