The honest answer is that it depends on four things, and none of them is the size of the house. It depends on how many people live there, whether any of them are small, whether there are animals, and how much of the maintenance the household does itself between visits.
Here is what each interval is actually for.
Weekly
Weekly suits a full house: several people, young children, a dog, or somebody working from home every day. At this interval nothing accumulates. Each visit is short and light, kitchens and bathrooms never reach the state that needs scrubbing, and the house sits at roughly the same level all the time rather than swinging between clean and not.
It is the most expensive interval per month and the cheapest per visit.
Every two weeks
This is the interval most households settle on, and it is the one to start with if you are unsure. Two weeks is short enough that a normal home does not get away from you and long enough that the visit is worth having. Bathrooms and kitchen floors are the things that decide whether two weeks is working: if they look tired by day ten, move to weekly; if they are still fine on day fourteen, four weeks may be enough.
Every four weeks
Four weeks works for a small household, an adult household, a second home, or a house where somebody is genuinely keeping up with the surfaces in between. It does not work for a busy family, and the failure mode is predictable: each visit turns into more work than the interval was priced for, and the house never quite feels reset.
Once, or seasonally
A one-time clean is the right choice for a specific event rather than a routine: before family arrive, after a party, at the change of season, before a house goes on the market, or after a project has put dust through the place. It is also the honest option if you want to see the work before committing to a schedule.
What changes the answer around here
A few local things push households toward a shorter interval. Road salt from December through March comes into every front hall and mudroom in the area and is hard on floors near the doors. Houses on gravel or a long drive take in fine grit all year. Around North Barrington, where many houses are on well water rather than municipal supply, mineral spotting shows on glass and fixtures within days of a cleaning. Wood-burning fireplaces put a fine ash on flat surfaces through the winter. Spring pollen coats sills and sunrooms for about six weeks.
None of those changes what a visit costs. They change how quickly the house stops looking cleaned.
You are not locked in
Start at every two weeks, watch the two rooms above, and move in whichever direction the house tells you to. A schedule is a plan, not a contract, and the interval that works in February is often not the one that works in July.