I haven't been down that way since 2002, but there was a major fuel station at the junction of the Cassiar Hwy (Rt 37) and the Alcan, west of Watson Lake. Another major fuel station on Rt 37 just north of the junction with the Stewart Hwy (Meziadin Lake). Once you reach Hwy 16, you are back in civilization and there are fuel stations in every town along the way and there are plenty of them.
In short, you have nothing to worry about on that route as long as you travel before Labr Day. After that, many stations in northern BC and Yukon shut down when they run out of fuel to sell. I think the ones south of Watson Lake are all still open, though. The Meziadin Lake area has lots of winter business (skiers, hunters, etc) and I think they stay open year around.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL