An object of the same mass has three different weights at different times. Which statement is possible?

If the object is at different places in the universe for the weight measurements then that's entirely possible. It would "weigh" less on the moon than on the earth. It would weigh differently on the planets. And, It might even weigh differently at different places on the earth, though my recollections of this are very vague. All of this assumes that bits don't fall off the mass, to make it, well "less massive".