Is gaining 4 pounds in 2 days considered sudden weight gain?

Yes! Anything more than five pounds (about 2.25 kilos) over the course of a week, which is an average of .71 pounds per day. If you can account for the gain, eating 3 bags of Halloween candy a day for a few days for example, then maybe it's not such a big deal. Otherwise, you should go see a doctor asap.