It is very common in Czech to spend your weekends „u babicky“. But he careful how you translate this information into English.
We don’t say that we are staying ‘by’ grandma’s house. If you say this, it suggests that she won’t allow you inside her house and you have to sleep in a tent nearby! No, you need to use the preposition ‘at’. So, the correct sentence is: „At weekends, I stay at my grandma’s house.“
But actually, one other thing. In fact, you don’t need to use the word ‘house’ at all. You can just say, „I stay at my grandma’s.“ That makes perfect sense in English and is actually more common that the full form.