My 60 days tourist visa expires on Saturday but the immigration office is closed on the weekends and I can't go to an Immigration office before that. Will I be fined 2 days overstay if I go on the Monday after? Or they don't take it into account since I'm going the first day they are open?

If you go on Monday, your permission to stay (it is not the visa you used to enter the country) will be extended, and you will not be fined. However, waiting until the last minute is not recommended. You will receive the same 30 days added to your original permission to stay whether you apply Thursday, Friday or Monday.