My Cat is getting Fat?

Hi im 12 and moved to the country side where I am now living with my nan, my cat came up to. My nan feeds her the normal ammount but my nan keeps giving her scraps of nans dinner/lunch/breakfast. She doesnt give her a LOT of scraps but a little. When my mum came up she said the cat has put on a lot of weight. Mum is thinking of taking the cat down with her and putting her on a diet but my mum owns a bird and that could be a little risky. Can you give me some info on what is healthy and light for my cat. Thanks, Thomas. PS: She is a medium sized cat and her diet consists of one cup of " Healthy choice " kibble and for her dinner we give her either Purr or Fancy Feast, she is a fussy cat and sometimes does not finish her meals. And my nan gives her scraps...