I found a simple way to test if it's a weight problem:
With no end mill (for safety), and your spindle powered up.. assuming it drops without Z-axis cmds, light press upward on the Z-axis with your finger trying to give constant pressure.

If it stops dropping, it's a weight issue.
If it still *forces* it's way down, it's something else.

You can also test this while traveling Z up or down. You should be able to hear the stepper motor has equal effort both ways when you counter the Z-axis weight manually.

Too much weight: Options are take some weight off, increase motor current, use more powerful motor, or different drive system.