It's true that making an incision through the soft tissues on the outside of the elbow changes the support for the elbow. This is usually a temporary situation. Unless there is a need to cut through all the major ligaments, your elbow should remain stable after surgery.
You will be immobilized for a period of time in a cast. When the cast is removed, there may be a rehabilitation phase with exercises prescribed by your doctor or physical therapist. It usually takes six to eight weeks to regain strength equal to that of the other arm. You can return to your weight-lifting program gradually, according to your doctor's recommendations.
It's a good idea to let your doctor know of your interest in weight training. This may influence the surgical method used and enable you to safely resume your program more quickly.