robotic arm doubt

Currently I am trying to build a robotic arm which consists of a base, two links and a gripper with low power servo motors

When I told my guide that  I am planning to use PID control and encoder for this he said that the link connected to base will have load of second link , gripper and the object which I am picking(200gm approx.). This would make that lower link unstable and it may even go down because of the load.

I was thinking of using high torque motors but that would increase my power requirements and cost.

My question is that, can this problem occur and if it does, wht can I do to avoid this. I am planning to use 12 V servo.