In a stronger gravitational field a given mass will have a larger weight.
An object's weight is given by this equation: #w=mg#
Gravitational field strength at a distance, r, from a centre of mass is given by this equation:
If an object is nearer a centre of mass then r will be smaller so g will be larger. In that case the weight of the object will be larger. If an object is moved from a distance R away from one centre of mass and placed a distance R away from the centre of a smaller mass then g will be smaller. In that case the weight of the object will be smaller.
A practical example: if an astronaut on earth has a weight of 833 N, on the moon he/she will have a weight of 136 N.
Using #m=w/g# the mass of the astronaut is #833/9.8=85 kg#.
So the weight on the moon (#g_M=1.6 Nkg^-1#) is: #w_M=mg_M=85×1.6=136 N#