Premise

I think that in most US states kids under 16 can get certain types of jobs. They can work for family members (not applicable in this case). For example one time in Cape May, New Jersey I walked into an ice cream parlour and saw three boys about 12 years old behind the counter who looked so similar they were probably triplets. I assumed their parents owned the ship.

And kids under 16 cam work as performers (also not applicable in this case) and do certain jobs like the chores they might do for their own families, like mowing lawns, or babysitting, for example.

And it is possible that Henry's job is illegal and they just haven't been caught yet.

I don't think that Swellview is very big on child protection, since the police were willing to lock up two thirteen year old boys and a thirteen year old girl in a cell with some men on Christmas Eve while not expecting any action to release them until the New Year at least a week away.

And is Henry actually described as thirteen in the first episode? Couldn't he actually be older? One time there was a cute and adorable looking blonde boy who was about shoulder height and looked about 12 working in a diner. At dinner at a fancy restaurant in the same village he said hello when working in the wait staff there. Someone asked if he as old enough to work there and he said he was sixteen.