If you say the weight = the force produced by the leadscrew and motor and ignore friction and inertia entirely then usually Force= pi/8 * TPI * Oz. In.
With 8tpi and 1200 OzIn Force = 3.142/8*8*1200 = 3770 oz or ~235 lbs F.
The screw will have an efficiency. If it's an Acme screw its about 30% so you will get 30% * 235lbsF or 70lbsF. If its a ball screw its about 80% so you will get 80%*235lbsF or 188lbsF.
If there's friction in the ways or the bearings then knock some more off...