Could someone please explain this to me?

I'm 17 5'5 and 115 Ibs and am planning to go down to 105-110 Ibs. The problem is, when i limit my calorie count to 800 per day, by the end of the week i usually end up gaining weight. Furthermore, i have friends who live in the tropics who are enviously slim, yet eat a very carb-rich diet (ie rice, beans, potatoes etc) could someone explain to me why this is and give me tips on how to healthily loose weight.