Short answer, to echo the other answers: it's entirely legal. Checkout time is checkout time, typically anywhere from 9am - 1pm (0900 - 1300). Depending on the situation, you may be able to extend this to within an hour or so of check-in time (typically 3pm), and a late checkout may or may be free. Factors which affect the situation include: what the arrival situation looks like for the next night (if it's a hotel that does a good business with weddings, a late checkout on a Saturday will generally be a minor miracle: wedding groups mean lots of early check-ins or at least attempts at such), membership level in the hotel's loyalty/rewards program, how much of a regular history you have with the hotel (4 one-night stays (especially if regularly spaced, e.g. every three months, as might be the case for a traveling salesman) generally count more for this than a single 14 night stay: the hotel will figure that you'll be coming back), the ratio of guests who have checked out already to guests with late checkouts, and how you made your reservation (in approximate order: directly with the hotel, through the hotel chain's website, through a credit card issuer's travel agency, and then basically everything else). If all else fails, a large tip for the front desk agent may get you a late checkout (in my earlier life behind a hotel front desk, for my rare morning shifts (I mostly worked night audit), I could most days get away with a total of 2 hours worth of discretionary late checkouts without getting yelled at by management or the housekeepers; a "$100 handshake" could reliably get one an extra hour).
None of this is any good for your situation: the best case for a late checkout is 3pm, hours less than you need. All is not lost, though. Depending on the hotel, there's a thing called "day use" or "zero night stay". If you happen to choose a hotel where the hotel figures they're able to flip the room and sell it again for the night, this may not be that expensive. The staffing practices of the hotel and their demand pattern are what govern day use availability. Generally, the more full-service the hotel is, the more likely they will have someone around in the evening to flip a room. If they're close to an airport or in the downtown of a major city, they're likely to be able to have someone walk in later wanting a room. On the other hand, limited service properties (e.g. motels), tend to have no one working at night besides the front-desk agent, so day use isn't an option (most hotel software will not allow a reservation for day use, by the way: generally the only way to do day use is to walk in or do it as an extension of the stay).
Beyond day use, most hotels will be willing to store your luggage etc. for a few hours, though it's best to bring up the possibility when you check-in. Factors which affect this are similar to those affecting whether you can get a late checkout, but you have a far greater chance of success.