Hello, Bear Bow Junkie. I did a little research on Mr. Barnes and found an ad in the September 1937 issue of Ye Sylvan Archer Magazine.
Willis H. Barnes lived at 601 N. 4th Street in Sturgis, Michigan. His ad reads like this:
Manufacturer of Big Game Hunting Tackle
"Barnes Bows held up perfectly in the recent Byrd expedition to the south pole. It was Barnes bows and arrows that brought down the big cats of Mexico in the latest big game motion picture called, "the Jaguar's Trail," starring Dan Brennan Jr."
"Hunters, write for information concerning new design bows and arrows."
If you can send me some pictures of the bow I'd love to see it.
Barnes was a contemporary of other bowyers such as Homer (Pops) Prouty, Earl Grubbs,Howard Hill, Cassius Hayward Styles (possibly the best bowyer ever),and Gilman Keasey.
I don't know what your bow is worth but it's certainly a piece of archery history and your lucky to own it.
Be safe.