I'm afraid you have me stumped on this one. I know of a couple of Arlies, but none that match yours. The closest match I can find is a female Arlie born in 1893 in GA.
I did find this entry, which confuses me:
1920 census Boyd Co KY p155a Scott Rigsby 38 KY/KY/KY wife Molly 38 KY/KY/KY son Arlie 17 KY/KY/KY
He's in the right place, but his age is off by 10 years. Not only that, I can't place this Scott. The only Scott Rigsby I know of was in Metcalfe Co KY in 1920.
There are only two Rigsby families in Boyd Co in 1900, Erastus and Larkin. Erastus has no sons under 14. Larkin has a son Henry age 6.
I think your Arlie is likely related to Larkin. Larkin was from a Rigsby family who were in Johnson and Lawrence Cos. He had a cousin whose son married Laura Bell McDowell and lived in Elliott Co, and a nephew who married Martha McDaniel and lived in Morgan Co. (All these counties are next to each other.) But unless Arlie is the same as Henry, I don't know how he fits in.
Sorry I couldn't immediately help. I'll let you know if I turn up any more information.