When you bill weekly - initially, a fixed 40 hr/week is assumed. But the client might push as much work as possible for that week...
Another option could be: Weekly (or monthly) billing + hourly for overtimes.
I do document parsing/data grooming so it's a lot of tweaking/fix as the client do the Q&A on the data.
Actually I overbook myself and offload some work to reliable part-time employees (the client is happy to known that not only me but other people are working on the project).
The overheads to doing a 10 minute fix are massive: they email/call you to make a request, you change work contexts, fix the issue, test and release it, notify them that you're done, keep track of the time you spent working, send an invoice at the end of the month, keep an eye out for payment, thank them for paying etc.
Rounding up to the hour mitigates this, but unless you're doing several maintenance requests per client per week, or are charging very high ($250+) hourly rates, your business is probably losing money by keeping this client on the books.
I think it's better to negotiate a monthly retainer that ensures making tiny updates is worth your while, and then just have a set-and-forget invoice that gets sent automatically every month for that amount. Even better if you can get paid by direct debit.
That being said, this question is more useful as an hourly rate since some people set their daily/weekly rate different because they work more or less than an 8 hour day / 40 hour week.
For companies that send you around the place internationally, I charge full days for international travel time - giving them the choice of sending you Business or Economy (and the corresponding amount of work that would be possible to undertake in flight).
EDIT: Re the last point - If they are paying by the hour/day/week, they are buying my time irrespective of whether I am able to work or not. Eg If they put me on economy, or put me through a day of meetings - they are going to be charged the day.