Green’s Dictionary of Slang

a debtor, one who goes out only once a week.

1821

‘An Amateur’ Real Life in London I 45: Your once-a-week man, or Sunday promenader, is one who confines himself, to avoid confinement, lodging in remote quarters in the vicinity of the metropolis, within a mile or two of the Bridges, Oxford Street, or Hyde-Park Corner, and is constrained to waste six uncomfortable and useless days in the week, in order to secure the enjoyment of the seventh, when he fearlessly ventures forth.