When you get to the top, you want to stay at the top. The problem is that on the way to the top, you became big. Real big.
Big companies can't maneuver well. An elephant can't do acrobatics. They know they can't compete head-to-head with smaller companies.
So big companies start to create artificial barriers to entry. They form partnerships (i.e. Google), they begin to advertise heavily (i.e. Superbowl), and they start to lobby the government (i.e. SOPA). All of these actions are there to create lasting relationships that will help a large company like GoDaddy compete with smaller, more maneuverable firms.
GoDaddy couldn't give a damn about SOPA. They simply want to have a solid relationship with various members of congress, the senate, and parts of the executive branch. I'll scratch your back, you scratch mine down the road.
Also, although I don't believe this is a significant motivating factor, SOPA would reduce legal costs for GoDaddy. Currently, if there's a court order for a seizure or something along those lines, it has to go through a process in legal. One of the features of SOPA, is that it would take the process out of the courts, at least initially. No courts = no court orders to process.