Sure, here are the suitable prepositions for each blank:

1. Would you like to go out? - No, thanks. I'd rather stay **at** home.
2. She's put **on** 2kg in the last month.
3. Sitting too close **to** the TV hurts our eyes.
4. Be careful **about** what you eat and drink.
5. My sister runs six miles every day to help keep herself **in** shape.
6. Watching TV too much isn't good **for** your eyes.