I like project-based billing but a lot of people don't, because it exposes them to risk (scope changes, unexpected complexities, client downtime) that they can avoid with time & materials billing. A weekly rate is, to a customer, pretty close to the same interface as a project rate, so if you're thinking about charging project rates, consider weeklies instead.
Also remember that part of the idea of upping your billing increment is not accepting piecemeal work.
Also remember that part of the idea of upping your billing increment is not accepting piecemeal work.