Each Tamagotchi has a minimum weight. If your Tamagotchi is too close to its minimum weight then it won't play games.
Let's pretend I have a Mizutamatchi. Mizutamatchi's minimum weight is 10g. If my Mizutamatchi weighs 10g-12g, I won't be able to play games. However, if my Mizutamatchi weighs 13g or heavier, I will be able to play games.