Question

Earths gravitational pull just got three times stronger! What happens to your weight?

Answer 1

Weight is simply the measure of gravity acting on an object. So, if the gravitational pull becomes three times stronger, your weight will increase (it will triple, in fact) because the measure of gravity acting on your body increases by three times. 

Answer 2

Your weight will be three times heavier.

Weight is the force exerted on a body by gravity. Weight is computed by multiplying the mass of an object by the force of gravity. If you were to triple the force of gravity, then the weight will be tripled as well. If you were to half it, then weight will be halved as well.