Why do some sims get fat and others dont?

It depends on average weight (what you set in CAS) and what they eat. The calorie system in 4 is fairly fickle. I suggest you look up a guide on it if you want avoid the dishes that put on weight.

Jog or use workout equipment a few times a week.
Or just give the sim a soccer ball and she will keep fit on her own !

Sims gain weight from eating in the Sims 4, even if you only feed them when they're hungry. Different types of food have different caloric values in the Sims 4 and determine how much weight they gain. If you don't want them to gain weight, you need to get them to exercise a few times a week.

Here is a list of the calories in different foods so that you can see which foods will make your sim gain less weight, although I'm not sure if it is up to date: https://www.carls-sims-4-guide.com/tutorials/calories.php

I'm not 100% sure, but I believe that jogging (either around the neighbourhood or on a machine) burns the fat more effectively that the strength building exercises. Carl's guide (mentioned by @georgia_simsx above) is a really good resource for that sort of thing.

Most of my sims in Cottage Living seem to gain weight really fast even though they are farmers.

Have a scientist give her Slimify serum. Make sure it's tested though! My Sim swelled up like a balloon last night from faulty Slimify serum. :lol:

Does walking make sims lose weight? (Like hiking/ walking the dog)
That should be a thing, I don’t want all my sims to have the fitness skill. ?

I let them buy a tub of slimming ice cream and store it in the fridge. Every now and then they like to grab a bowl of ice cream from the fridge and I don't get mad about it. ? I also don,t mind if they drop everything and do some crunches in the middle of whatever or wherever. Sometimes I send them jogging. So far, my formerly fat sims have managed to keep in shape.

Also, opposite to gaining weight, if a Sim only eats junk food (like when in college and all they have is the mini fridge), they will become malnourished.

Female sims will also gain a little weight with pregnancy and sometimes it stays on after childbirth.