In a multi-level model, are larger clusters given more "weight" than smaller clusters? Let's say I'm estimating the effects of a tutoring program on students clustered within schools. For the sake of the example, let's say I have data from two schools, a smaller school with n=50 students and a larger school with n=500 students. The effect of the program within the smaller school is large (d=.5) but the effect of the program within the larger school is small (d=.1).
When I use a multi-level model with these data, does the fact that the larger school have more students give it more weight in my ultimate estimate? Or is the multi-level model only working off of the means of the two groups? In other words, should I expect an overall estimate closer to d=.15 or closer to d=.3?

Larger clsuters are given more weight, so in your example, you should expect an estimate closer to d = 0.1 than 0.5
