Hi.
If you are afraid of those weights, put them on a spot where they don't count that much.
Perhaps all of the servos close to servo 1, and have some mechanical way to convey the movement of the servo.
Think of wires or rods.
Also try to imagine how muscles actually work, they seem to do that job quite accurately and reliable.
So perhaps mimicking that would be a smart move.
I would also do the same thing to the arm connected to servo 1, because you probably need more speed on any axis than a servo could deliver.
Sorry, got an emergency call (don't worry, no lives at steak) and have to rush to work now.