1. What is the reason that we stand on Erev Shabbat for Mizmor leDavid?
2. Also why do we stand for Aleinu?
1. There is no hova (requirement) to stand when saying any mizmor from Tehillim; this applies to the mizmor you mention which we recite on Erev Shabbat, as well as to any perek from Tehillim on any other occasion. I am not implying that it is not a hova, but is nevertheless a mitzvah. I mean that it makes no difference if one stands or sits.
2. The recitation of Mizmor Shir leYom haShabbat, like any Mizmor Shel Yom, is not a hova. It is an ancient and beautiful minhag (see Meseket Soferim 18:1-2) based on what was recited in the Mikdash by the Levim (see end of Mishna Tamid). The fact that it is not mentioned in the Tur (OH 267) or in Sidure Hakhme Ashkenaz indicates that it is a later minhag.
3. Reciting Aleinu at the conclusion of a minyan is also a minhag, which the Tur (OH 133) does mention. Both reciting it and standing whilst so doing is not a hova, despite what the Rama writes (OH 133:2) in the name of the Kol Bo. If one does choose to perform this beautiful minhag then one should do so with kavanah.
4. Nevertheless, in a minyan where everyone stands one should not remain seated. Even though it really should not concern anyone, the fact is that it does, and the Hachamim teach us that in public one should not act differently from the community so as not to cause mahloket.
29th of Elul, 5770 Wednesday, 08 September 2010