The invention relates to a drilling rig comprising: a tubular stand support tower, tubular stand storage rack, slip device for supporting multiple tubular stands, and a tubular stand connecting device. According to the invention the rig is provided with a tubular stand handling system, adapted to move a tubular stand between the storage rack and a position in the firing line above the tubular string slip device, and adapted to rotatable support the tubular stand in the firing line during spinning in, to allow for connecting the tubular stand with the tubular string, and during spinning out, to allow for disconnecting the tubular stand from the tubular string, the tubular stand handling system comprising. The tubular stand handling system comprises vertical rails and a lower motion arm assembly and an upper motion arm assembly comprising grippers, mounted on said vertical rails. Also provided is a weight compensation control system.