Why am I experiencing fine hair growth after my second laser treatment?

Laser hair removal should be a series of 6-8 treatments. We know that the hair growth cycles is between every 5-6 weeks so you should be making appointments around that time to zap the hairs. 

You have nothing to worry about, the treatment is acting as it should. Because your hair grows in cycles, lasers can only treat hair that is actively growing. In effect, this means that after each subsequent treatment should experience less and less regrowth until you are satisfied with the results. As finer hair is more difficult for lasers to target, these hairs tend to survive longer in the treatment process. Each person’s hair regrows differently at different points in your hair’s growth cycle, this may partially explain why you did not experience as much regrowth of finer hairs after your first treatment.
That being said, if you continue to have questions there is no substitute for an in-person consultation with your provider to go over any questions you have about your results or treatment.

This sounds good.  You want hair to come back finer after each treatment; until it doesn't come back at all.

This is common with laser hair removal as the old dark coarse hair can be replaced with fine “peach fuzz” type hairs.  The laser will continue to work on the dark coarse hairs; but if they are too fine and not dark enough the laser will not see them to treat them.  You may need to wax or use electrolysis for those hairs.