I am not sure "overweight" effects your game as much as "out of shape". I think there is a big difference. Someone can weigh 250 plus and still be very smooth on the mat. Someone else can be out of shape and under 200 and not last long at all (cardio wise) Check out
www.niagarabjj.com , Esfiha is about 280 / 300 and he moves like 165 lb guy on the mat, however when he uses his weight, it is not good!