How does one play an opponent with a big backhand? There are several versions of this type of player. Some have big backhand smashes and seem to be able to smash anything from that side. Others don't hit quite so hard but keep coming at you with it. Others have big backhand loops. In each case you are faced with an opponent whose backhand is stronger than yours, and is a constant threat to win the point. You have several options, and you can (and should) use more than one of them.
Compared to the forehand, the backhand is often a cramped shot because the body is in the way. And so the enemy of the backhand is depth. If you keep the ball deep on the table, few players can attack that ball as strongly as they can off a short ball. This is the most common reason for an opponent with a big backhand - balls that aren't going deep, thereby giving the opponent opportunities for big backhands. (Note that depth is the first item listed, but keeping the ball low isn't even listed as one of your options. That's because it's assumed that you are trying to keep the ball low. The exception - deep, arcing loops with heavy topspin are effective against most big backhands despite being high.)
2) Play the Forehand
The most obvious thing is to simply play the forehand side. The problem here is that even with a big backhand player, the forehand might be pretty powerful as well. So figure out early what shots the opponent has trouble with on the forehand, and play those shots there. Often the forehand side isn't as quick as the backhand, and so quick, angle shots there are effective.
3) Play the Forehand, Come Back to the Backhand
Many players have strong backhands when they are in position. So draw them out of their backhand pocket by going to the forehand first, and then coming back to the backhand. (Ironically, this is also an excellent way to play a player with a big forehand - draw them out to their forehand side, then make them play backhands.)
4) Attack First
If you have good serve and receive, you can most often get the first attack. There's nothing like a good first attack (again, deep on the table) for stopping any type of attack by the opponent.
5) Attack the Middle
Make the opponent move side to side to hit those backhands by playing both wide to the backhand and to the middle. (The middle is the mid-point between forehand and backhand, roughly where the playing elbow is.) This forces the opponent not only to move, but to decide between forehand and backhand. Players with big backhands often favor the backhand even on shots that go somewhat out to the forehand side, and so their "middle" might be toward their forehand side. Find that spot and go for it. The more table the opponent tries to cover with the backhand, the more you can make him move.
As long as you keep the ball deep on the table, and perhaps move it around some (wide backhand, middle, wide forehand), a consistent backhand can often beat a more powerful one. Don't try to be quicker or more powerful than the opponent with a big backhand; out-steady him while keeping the ball deep and making him move.
7) Changing Spins
Few players have powerful backhands against both backspin and topspin. Find the spin they have the most trouble with, and place it deep on the table. Or go back and forth between deep, spinny loops and deep, heavy pushes to force him to adjust to both.
And finally, there's an eighth option.
8) Develop your own big backhand