When 38.0 mL of 0.1250 M H2SO4 is added to 100. mL of a solution of Pb(NO3)2, a precipitate of PbSO4 forms. The PbSO4 is then filtered from the solution, dried, and weighed. If the recovered PbSO4 is found to have a mass of 0.0471 g. What was the concentration of nitrate ions in the original solution?

Mass is the amount of matter in an object.  weight is the measurement of the pull of gravity on an object.  say for example, you travel to the moon which has a different gravitational field compared to the gravitational field of earth. (gravitational fields: earth = 1, moon = 0.165)  now when you are on the moon, the pull of gravity on you is different than on the earth. and as weight is the measurement of the pull of gravity on an object, that means yes, your weight can and will change on the moon.  however, on the moon, on earth or even on jupiter, the amount of mass inside of you remains the same. meaning your physical mass remains constant.  in conclusion it is possible for your weight to change as your mass remains constant. 

Density and pressure