The Tefilin Shel Yad is supposed to sit on the lower half of the bicep of the non-dominant arm. A standard-sized bayis (50 mm) has a base that is about 68 mm long. On many Bar-Mitzvah-age boys (as well as adults of slight stature), there is not enough room on the lower half of the bicep to hold a standard sized bayis, so part of the bayis rests on the upper half of the muscle. Many Poskim hold that the entire bayis must rest on the lower half of the muscle. To comply with their opinion, it is possible to get a Shel Yad with a base that is 42 mm × 60 mm (about 20% smaller).
note: The Shel Rosh would be 50 mm regardless – making it smaller involves many technical and halachic difficulties. There is no halachic reason for the batim to be exactly the same size.
A smaller Shel Yad should not add significantly to the cost of a pair of Tefilin.
-= 8 =-