Why is weight so important?

[BrentJ]

It can also be a weight / power trade off.

Eg to get a robot moving at the same speed at different weights takes different amounts of motor power. By making the robot lighter you may be able to use lower power ( cheaper ) motors.

Also if the motor doesn't have to generate as much force ( torque ) to move the robots then you use less electrical energy from the battery. So the battery charge lasts longer or you can use that energy somewhere else like a stronger / faster motor for the arm.

Materials is also another area where you can save money.
To keep it simple I'll use an example of castors.

Say you have 100lb robot on 4 castors. So say you decided you need 25lb castors ( 4 * 25 = 100lb) to spread the weight ( we're ignoring a lot of things to keep this simple ) and they cost $10 each = $40. But you lighten the robot to 80lbs now you could use 20lb castors at $8 each = $32 a saving of $8. Not much of saving but every bit counts.

Also a lighter robot means you can ship more spares / tools in your crate.

I know this is an over simplification but I hope it gives you the idea.

It's a matter of balancing everything out.
Like you wouldn't try and tow a caravan over the Rockies with a British Mini car. In the same way you wouldn't use a Kenworth truck to tow one of those luggage trailers you see towed behind mini vans.