I know this has already been answered, but I'd like to contribute what I had in mind (this is my first post on this SE so please tell me if doing this is acceptable (that is, discussing other possible answers rather than stopping at the expected one)).
Instead of writing "your exact weight", he writes out all possible weights on the sheet (since he hasn't imposed time restrictions) and then asks the boy if he has in fact written his weight on the piece of paper. The boy is then compelled to say 'yes' since at some point, the man did write his weight on the paper.
Here are 2 potential problems with this solution:
The piece of paper is not large enough to write all these numbers (fair enough, but again, since there is no time restriction, the man could write some numbers, erase, and then write some other numbers and so on. When he is done, he still asks the boy if he has written his weight on the piece of paper.)
"All the possible weights" involve an infinite amount of possible numbers (as the exact weight is probably an irrational number). Also fair, but I would argue the boy doesn't know his exact weight either; I would also argue that like most people, an integer number would suffice as a reasonable answer (so the man only has to write integer numbers taken from some interval fit for a child)
Anyways, just wanted to share.