There is no fixed rule or formal method to estimate and tune the weight matrices Q and R. It is an iterative process wherein you will have to see your plant time response wiith respect to desired performance criteria and adjust the weights accordingly.
However a good way to start the process is by using Bryson's rule wherein weights of Q matrix determine the error permitted in each output state and weights of R matrix determine to control effort. Keep a track of the cost function for each selection of Q & R and keep it to minimum possible.
Example: You can take following matrices as initial estimate for a 8x8 system (i.e. 8 output states) with 4 control inputs when you want to control only the last four states;
Q = A* diag(0 0 0 0 1 1 1 1)
R = B* diag(1 1 1 1)
where A & B are scalar factors.