Tips to gain weight (muscle weight) for Boxing?

Never put down the protein. Always continue consuming protein and eating good sized portions more than 5 times a day(in a well divided proportion to a larger 3 meal a day plate.) Research different types of proteins and not just powders and supplimrnts, but what you can find in regular foods. Your weight is going to come from your diet. So make sure you have the best one possible. Keep in mind that you may find a need for more speed and agility. So a more lean, dense muscled physique could be necessary, not just bulky muscles. You may be small, but that's why there are weight classes. You don't want to aquire a large bulky physique just to make up for a small man's complex or some crap. There are differnt types of boxers and techniques, so find which one may work best for you. Good luck.

Lift Weights and Eat a lot of Protein

Short answer, eat, lift, sleep. Eat like an animal, lift like a God and sleep like a baby.