Claimers may run more often than Stakes horses but just scanning some PPs I have left over from the Keeneland Spring Meet, I'd say three weeks is the usual minimum.
I just happen to remember (fondly!) a bottom level claimer named Bullyampa that ran in NY back in the 60s. He ran on September 27, 1967, the date of the great race (The Woodward) that featured Buckpasser, Damascus and Dr. Fager. I have the PPs from that day. Bullyampa was making his fifth start in September!
ML/NJ
My experience around here in MD is they can run weekly, definitely 2weeks.
Not that it was unusual in his day, but one of the great things about Man oWar was his schedule. He had 2 days between stakes once as a 2yo and raced often with about 10 days between, even as a 3yo. At 2 he ran at Saratoga every week, and twice as 3yo (4wk-meet). Never mind his record-setting rate as a 3yo or the fact every race but his maiden was a stake race.