If the tension in the cable of $1000 \,kg$ elevator is $1000 \,kg$ weight, the elevator
Is accelerating upwards
Is accelerating downwards
May be at rest or accelerating
May be at rest or in uniform motion
If the tension in the cable of $1000 \,kg$ elevator is $1000 \,kg$ weight, the elevator
Since $T= mg$, it implies that elevator may be at rest or in uniform motion.