"Get out of my forest Bill, you are not welcome here."
"Alright, alright. But remember if ya see any twins... call me up Wirty."
Headcanon time!(this is a long one.)
Before the events of Over the Garden Wall take place the Beast as we know was the protector of the forest, he kept the forest alive and helped stray kids find their ways out of the forest using his lantern. However, Bill Cipher wanted something from the Beast and when the Beast refused, Bill cursed the beast and the forest, turning he Protector into a monster. The Beast now takes the souls of lost children and makes them apart of his forest. Then the events of Over the Garden Wall take place and the Woodsmen blows out the light in the Lantern that the protector once used, lifting the curse but still killing the Beast. The forest soon began to slowly die after Wirt and Greg returned home. So the Woodsmen would take the Lantern and go walk through the forest at night, as the Beast to give the forest life.
Wirt and Greg lived long human lives and once they died, since their souls were temporarily trapped in the Unknown, their souls were bond to the Unknown and they return as the age the had first came as. (Wirt being 15 and Greg being 6-8) Wirt is the first to return and notices how more lively the forest is as we walks through it. He stumbles upon the Woodsmen's Mill/Beatrice's house and finds his old companion. He and Beatrice talk and catch up until sun down, where Beatrice suddenly stops in the middle of her story to watch the Woodsmen, draped in black, begin his walk through the woods. She explains to Wirt that becoming the Beast has becoming harder and harder for the Woodsmen and that he won't be able to keep it up. Wirt stays up and watches as the Woodsmen comes out of the Forest at sunrise where he passes out. Wirt runs out to helps him with Beatrice not far behind. Wirt from then on takes the roll as the Beast and walks the forest every night.
There where a few times he met with Bill who tipped his hat and asked him for something. Wirt shrugged it off every time he asked. And soon Wirt stopped allowing Bill to roam the forest undetected of uninvited.
Years later Dipper and Mable get into a fight with Bill and their souls are sent to the Unknown where they met Wirt, who escorts them to Beatrice and she takes care of them. The twins stay with her for a few nights when Dipper notices that Wirt leaves when the sun goes down and comes back when the sun comes up. He follows Wirt on night and watches as he takes the Lantern and turns into the Beast. Dipper follows Wirt until he meets up with Bill again. The two talk and Bill starts asking for Dipper and Mable in the Bill sort of way. It makes Wirt mad and he tells Bill he is not welcome.
(Over the Garden Wall and Gravity Fall are not mine)