Hei Bai's last ability doesn't cause you to move counters from Hei Bai onto the target creature. Rather, you put the same number of each kind of counter Hei Bai had when he left the battlefield onto the target creature.

Hei Bai's last ability puts all counters that were on Hei Bai onto the target creature, not just his +1/+1 counters.

If Hei Bai has -1/-1 counters on him when he leaves the battlefield, that ability will include those as well. This may result in the recipient of the counters dying.

In some cases, you may end up putting the appropriate counters on more than one permanent. For example, if you control a Buzzard-Wasp Colony when Hei Bai dies, you'll put the appropriate number of each kind of counter onto both the Buzzard-Wasp Colony and the target creature. If you target Buzzard-Wasp Colony with Hei Bai's last ability, it will receive counters from both abilities.

If enough -1/-1 counters are put on Hei Bai at the same time to make his toughness 0 or less, his last ability will see all of the +1/+1 counters he had when he left the battlefield as well as the -1/-1 counters he had, and an equal number of each of those types of counters (plus any other applicable counters) will be put onto the target creature.