I think it really depends on where you are (geographically) conducting the study, who are the users and how tedious it is to fill the diary.
If it takes lots of writing to describe all the interactions with the app, users may feel the same compensation too small compared to if the diary consist of, say, just a 3-state-smiley-face -feedback.
Generally students may be satisfied for smaller compensations than full-time workers. If not, the study sounds too big and might need to have smaller scope or done in multiple parts. For the studies I've participated, I'd say that 2-4 movie tickets or a ¤40-60 gift certificate to e.g. Google Play store should be appropriate. (I would be horrified to log about every action with my phone for three weeks, though!) In developing countries the compensation should be adjusted to the common income level, not to cause any biases.
Also, countries may have different laws about taxes for gift-like compensations (i.e. no taxes up to some fixed sum per year per person).
One way to measure whether the magnitude of the compensation is right is to state the sum/gift and assumed work amount upfront. If users know what they are expected to do and what they get in return, they are generally happy if they enroll. Then again, if nobody is interested, you may need to either increase the compensation or decrease the amount of work.