I can't tell you how to deal with a bigger opponent in general, but here's a technique I learned from someone who is much smaller than me. He constantly has to deal with people who outweigh him by over 40 pounds. Please excuse my poor grasp of terminology. If anyone else can describe this better, please help me out.
This is going to be an arm bar. the important part is keeping him in close. You've probably seen the arm bar before.
He'll have to be in your guard for this to work the way I learned it. Wrap your left arm over the top of his right shoulder (is this called an overhook wizzer?). Keep him in tight to avoid strikes. Put your left foot on his right hip, push down and rotate your body as far to his left side as possible while maintaining your overhook. As you rotate, kick your right leg up under his left armpit. The lower part of your leg will be over his back, keeping him in tight. For the finish, throw your left leg over his head and rest it on the left side of his neck. Arch your back for the finish. If you aren't flexible enough to get your leg over while keeping the overhook locked down, let go a little at a time, allowing him to pull his arm out a little at a time until you have enough distance to pop your leg over his head.
I know this is a difficult description to follow, but I can't find a video of this on youtube. I've used it against big, strong opponents and I've had a lot of luck.