Not beeing able to lift heavy weights in a problem. As I personally lift pretty much pure strength = 5x5x85% of my maximum.
So a program could looks like this:
Sit-ups with extra weights 4x~10 reps
Sit-ups with a twist 4x~10 reps with extra weights again (5 on each side that is)
Calfs 4x~8.. I don't train them hard atleast, but I guess they are good if you want to have a strong guard (I favor the open guard).
Clean 5x5x85%/Pull-ups with extra weights 5x5
This programme I do for 6-8 weeks. After which I do a 3-4 weeks programme of explosiveness.
Meaning the same moves but the reps are 4x6 and I reduce 10-15% of the weights. The main point is to do those big muscles clean andexplosivly. If you want to improve your explosivity avoid also beeing so tired that you get lactic acids in your muscles.
Then it's very good to train stamina after MMA/BJJ/Kickboxing/Whatever- training with high intensity and alot of lactic acids involved
Take like 40lbs weights and do all kinds of workouts. You can always ask your trainer for tips.
PS. My own programme doesn't look like this as I have to compensate alot of moves with other ones due to my back problems...