It's an old expression, been around the Ozarks(probably in other areas too)for a long time. It's a mildly derogatory description of something or someone that a person doesn't think too highly of, such as "I threw that suckerbill away," or "Tell that suckerbill to hit the road," or "That suckerbill doesn't know what he's talking about."
sucker
a sucker a sucker
Hooks and sucker rings.
A "sucker" is a gullible person, as in "There's a sucker born every minute". "I'm a sucker for .." means one is vulnerable to or easily attracted to ...
Sucker barb was created in 1860.
Longnose Sucker was created in 1773.
June sucker was created in 1878.
Super Sucker was created in 2003.
White Sucker was created in 1803.
You can say "À plus, naze!" in French for "See you sucker".
pearsons
A sucker's bet is one that can't be lost - you're a "sucker" because you think you can win, but you can't.