Does lifting weights help to hand balance? The answer is yes and no.
Let me qualify all the following by saying there are many different ways to lift weights. Whether you are doing power lifting, Olympic lifting, bodybuilding, or just good old fashioned strength training with barbells and dumbbells. How you lift matters as much as anything.
Certain exercises are going to help you out. And others won’t do much for you.
Specifically for pressing movements. It requires a tremendous amount of strength to be able to push your bodyweight overhead. You need strong triceps and shoulders.
Since many presses take you through different planes of movement, not strictly overhead work, such as a press from half planche to handstand or the frogstand press you will also need strong pectoral muscles. Of course your back and abdominals are used to keep you stabilized.
If you use weights to make these muscles stronger than you will be able to do these stunts easier.
Of course hand balancing takes a huge degree balance. While weightlifting can help your coordination, it is nothing compared to what you need to stand on your hands.
Being able to press a heavy barbell overhead has no carryover to being able to hold a handstand.
A handstand is a skill and needs to be practiced in order for you to get good at it.
These days many people are moving away from weights because they think they are not functional. To that I have to say it all depends on how you use them.
Whether you decide to build you upper body strength with barbell presses or with handstand pushups is up to you. They both build strength.
Spend some time using both and see how well they work for you.
Professor Orlick outlines a full on course of barbell, dumbbell, bodyweight and other exercises in Hand Balancing Made Easy. If an accomplished hand balancer like him believed in them, than there surely is value in the exercises.
In addition, in the interview I did with Jim Bathurst he talks about his favorite weightlifting exercises and which ones carryover to his hand balancing best.
Good Luck and Good Hand Balancing,
P.S. Professor Orlick even has some very creative weightlifting exercises to help with the one hand handstand. Now you can get How to do the One-Hand Handstand by itself.