It wouldn't be uncommon to find a discrepancy between sides. The
question is whether it's a difference of strength or for some other
reason, e.g., a compensation for an old injury or something along those
lines. One could do as you suggest and work the weaker side a little
extra, but most of the time, just working both sides equally will help
the weaker side catch up. As long as the difference isn't huge, it's
OK.
Done with opposite hand and leg, this movement is often quite revealing,
and it doesn't need a lot of weight to be effective - I often practice
it with no weight at all, just touching the ground with the opposite
hand or both hands.
-S-