Is it common to gain weight after tubectomy?

It is difficult to believe your weight has increased by 4 kg within 12 days of tubectomy. Tubectomy does not cause this. You need to consult a physician or endocrinologist to check you do not have some endocrine problem. If there was no problem during the surgery, especially if it was a laparoscopic surgery, you can start exercises. However, it is advisable to get a clearance from your gynaecologist before starting exercises. Also, the type of exercise you require would best be decided by a physiotherapist.