Must one stand when donning a Tallis-even if he is not saying a blessing? The donning of the Tallis must be done in a standing position. Thus, one is to stand when wrapping a Tallis even if a blessing is not being said [such as after re-wrapping the Tallis after using the bathroom and the like].
Must the Tallis Katan be worn in a standing position?
Some Poskim rule one must stand also when putting on a Tallis Katan, even if a blessing is not being recited. Thus, when placing the Tallis Katan on in the morning, or upon awakening, or after Mikveh, one is to stand. Others however write that this law does not apply to a Tallis Katan, thus justifying the custom of many not to be particular to stand while putting on a Tallis Katan.
Must a sick or weak person stand when putting on a Tallis?
 8/2; Siddur Admur; Michaber 8/1
 Siddur Admur
 The reason: As all blessings said over Mitzvos must be recited in a standing position. [Admur 8/2; Beis Yosef 8 in name of Yerushalmi and Orchos Chaim Tzitzis 27; Haittur Zohar Tetzaveh brought in P”M 8 M”Z 1; M”B 8/2] The reason for this is because a blessing is considered similar to Avoda in the Mikdash. [Eshkol 83; Abudarham; Bach] This however is with exception for the blessings made over Shechitah and Challah, being that these two Mitzvos don’t hold the same weight as other commands, as they are done merely for the sake of being able to eat food. [Admur ibid; M”A 8/2] The above however is only with regards to the blessing of a Mitzvah, however the Mitzvos themselves, some are not required to be done standing while others are required to be done standing, as will be explained in each relevant section. [Admur 8/2] Vetzaruch Iyun according to this ruling here why we are accustomed today to sit by various blessings of Mitzvos, such as “Al Achilas Matzah”; “Leishev Basukkah” and others. See Bach 8; Pnei Yehoshua Megillah 21a; Mor Uketzia 8; Piskeiy Teshuvos 8/4 who differentiate between Mitzvos that are performed standing versus sitting.
Other opinions: Some Poskim rule that the blessings of Mitzvos are not required to be said in a standing position, with exception to those Mitzvos that must be performed standing. [Artzos Hachaim 8/1 states it is only a Mitzvah Min Hamuvchar; Bach 8 requires only Mitzvos that have no benefit; See Pnei Yehoshua Megillah 21a; Mor Uketzia 8 that depends it if the Mitzvah is accustomed to be performed standing; Piskeiy Teshuvos 8/4]
 Implication of Siddur Admur and Admur 585/1 regarding Shofar; Tzemach Tzedek in Piskeiy Dinim 407; Chayeh Adam 12/3; Kitzur SHU”A 9/13; Poskim brought in Kaf Hachaim 8/5
 8/4; Siddur Admur; M”A 8/2; Olas Tamid 8/1; Elya Raba 8/2; Poskim in Kaf Hachaim 8/4
 The reason: This is an institution of the Sages. The Sages based this on a hint in the Torah, as the verse states “Vehaya Lachem” by Tzitzis and “Usefartem Lachem” regarding the Omer. This comes to teach us that just as the Omer must be counted in a standing position [as explained in 489/4], so too the wrapping of Tzitzis must be done in a standing position. [Admur ibid; M”B 8/2; See Minchas Elazar 1/48 and Piskeiy Teshuvos 8/4 footnote 30 for sources in Geonim and Rishonim for this Derasha, although it is not mentioned in the Talmud] This however is only with regards to the Mitzvah of Tzitzis, however by other Mitzvos, some are not required to be done standing while others are required to be done standing, as will be explained in each relevant section. [8/3; See Piskeiy Teshuvos 8/4]
 Piskeiy Teshuvos 8/3; However see Q&A below regarding Tallis Katan that some learn only the actual Atifa must be done standing and hence when rewearing the Tallis without doing Atifa, such as after the bathroom, one does not need to stand. Vetzaruch Iyun!
 Based on Admur 585/1 regarding Shofar and the same would apply here by Tzitzis as the entire law of standing by Shofar is derived from Sefira to which Tzitzis is juxtaposed!
 The reason: As in such a case, this leaning is not defined as standing but as leaning. [Admur ibid; See also 607/7]
 Makor Chaim of Chavos Yair 8/1; Sefer Hayireh of Rabbeinu Yonah 7; Setimas Haposkim; See Piskeiy Teshuvos 8/3
Ruling of Admur: On the one hand Admur writes “when wrapping” hence implying that only by the actual Atifa of a Tallis Gadol must one stand, and not when simply wearing a Tallis Katan, or even when re-wearing a Tallis Gadol without Atifa. On the other hand from the reason of Admur ibid seemingly there should be no difference, as the “Lachem” teaches that the Mitzvah of Tzitzis is to be always be performed while standing. Vetzaruch Iyun!
 Minchas Shlomo 2/4-6; Halichos Shlomo 3/8 and 9
 The reason: As only when one is wrapping the Tallis like a Yishmaeli was the standing required. [ibid]
 Aruch Hashulchan 8/3; See also Lehoros Nasan 12/3