Sig is a mean-looking dog that you find in your path to Amelia's father's house after you leave Mr. Starcher's barn. You remember a line Amelia once said that gives you insite into getting past him.
“Aww, Sig looks mean. But just remember, he’s a sucker for a few table scraps…”
You must go and find the sadwiches that Amelia and you ate during your adventure in the barn. Climb into the rafters and walk carefully across to the other end of the barn. There you will find the sandwich, hidden behind some boxes. Go back to where Sig was located and feed the sandwich to him. He will never return to bother you again.