For the sake of the topic, I won't go into full detail to the symbol of the apple in human culture as a whole. I will only focus on one point, and that's the fact that the apple symbolizes Knowledge (due to the bible, with the forbidden fruit and all).
You can easily find a lot of pictures of apples being associated with books or pencils, being used as a graphic for schools (mostly kindergarten, or primary school), and because of that, you can loosely associate them with children.
Now for the two examples mentioned in the question:
- In Hello Kitty's case, it is a show aimed for children; so it makes sense for them to use Apples as an alternative over using actual units of measurement, you could say that they did it for the "Cute" factor.
- In Mekaku City Actor's case, Marry Kozakura is a somewhat child-like character (and Kawai too); so you can use THAT as a reason for using apples to state her weight. Or simply, it's rude to state a lady's weight; so the creators did it like this as a "joke", and the reason they chose Apples instead of other fruits is the same as in Hello Kitty, for the "Cute" factor.
another factor could be that, an apple's weight and size is common knowledge; but that's just secondary at this point.