Can i weight lift even though i have diverticulitis?

Within reason: Disease convalescence is viewed very differently today. Not many docs tell their patients to stay in bed till they are completely well. When you are feeling good enough to exercise, please do. Just don't over do it to cause yourself harm. The general recommendation is usually to bring up the level slowly as tolerated.

Yes: If it doesn't hurt you, absolultely. Use pain as your guide.