true or false weight is the measure of the pull of gravity

Actually it should be true. The mass of an object is the same no matter where the object is located (Earth, moon, space, etc ...)

Weight, on the other hand, is the measure of mass when affected by gravity. So the weight of an object on the moon and on earth will be different due to gravity. So, weight is in fact the measure of the pull of gravity.

The answer should be true. It is important to understand that mass and weight are not the same.