My 9 year old son has had a hoarse voice for about 6 weeks. What could be causing it and should we see a doctor?

Hoaseness for 6weeks. Any hoarseness of more than 3 weeks at any age should be checked by your doctor. The commonest cause of hoarse voice persisting more than 3 weeks is silent gastro esophageal reflux, there can be other causes even at age of 9, like polyps of vocal cord, overuse of voice in singers, and viral leryngitis so see your doc or an ENT specialist.
See your doctor. Hoarseness in kids can be caused by a variety of different things: overuse (screaming, yelling), allergies, post nasal drip, reflux (stomach acid coming up the throat), and nodules on the vocal cords. 6 weeks is long enough to see if it goes away on its own, i'd recommend seeing a doc for this one. Best of luck!