RMFRP, page 35 says the following:
Weight Penalty
If your character is not very strong and attempts to carry too much equipment, your Gamemaster may require you to calculate your character's "Weight Penalty" (see Section 18.16, p 56). If your character has a weight penalty, it will modify his base movement rate and his MMP.
emphasis mine...
So, the answer to your question is Yes, weight penalty is added to BMR.