
Sadly cats are very independent and will choose where they want to live ...who knows what goes on in thier heads!.
I have 3 cats of my own and 1 cat that lived in our road but moved in with us about 2yrs ago we did everything to discourage him but he was determined he used to sneak in the back or sit by the front door then jump ontop of the kitchen units to sleep where we couldnt get to him.
The dogs dont bother him and he isnt frightened of them.
His owners to be honest couldnt care less about him they knew he was being fed at our house we dont think he was being treated very well as the family like to drink ;)
She still refers to him apparently by other neighbours as her cat but he wont go home.
I never refer to him as being mine eventhough I love him to bits he's very affecionate but I couldnt leave him out in the cold we just leave him to do his own thing if he comes in thats his choice whereas my cats I have rules that they cant stay out at night.
Your cat is a differnet situation as he was loved and cared for and you want him back well I say "just take him" if you have left a note on the collar to let the people know that he belongs to you just in case he returns to them.
If he is overweight maybe he has a few different homes he visits for treats I know one of my cats visits a certain friends (neighbour) house early morning and they give her some ham and milk on a regular basis but I know about this it sjust a friendly visit!
You might find that quite a few people think he belongs to them!!!!!
I would take her back and put her in a room with a tray and food for a few weeks get her out of her old routine get the weight off her give her lots of love and attention and hopefully she'll be fine.
Roni