Q. Is there any truth that one should be machmir to fast on Asarah Beveth more than another taanith? Therefore, even someone who because of age and weakness does not fast besides Yom Kipur and Tishaa Beav, should fast on Asarah Beteveth? If correct why is that so?

A. Beis Yosef (O.H. 550) quotes Avudraham’s opinion that if Asarah Beteves was to occur on Shabbos we would fast on that day, since it is similar to Yom Kippur in which the pasuk mentions “beetzem hayom haze” (Yechezkel 24).
Toras Chaim (550: 4), wonders why Bais Yosef would mention the above detail since it does not have a practical difference, as this fast day cannot according to our luach coincide with Shabbos. He explains that it may be for the purpose of being more stringent on this taanis than others and other prohibitions, such as washing also apply. He mentions that his own father, the Machane Chaim, on the end of his life, when he was very weak and was not supposed to fast, he forced himself to do so on Asarah Beteves.
Biur Halocho (551: 1) mentions that some maintain in Asarah Beteves the stringencies of the Nine Days.
Ratz Katzvi (16) maintains that on this taanis a baal nefesh should begin fasting from the night before. Weddings should therefore be avoided on that night.
Bnei Isoschor (Teves14) explains that this fast day marks the very beginning of the churban and all the days of avelus that we maintain, and is therefore more severe and strict.
However, in practice many Poskim maintain that one does not have to be more rigorous than in other fast days (Shulchan Aruch and Mishna Berura 550:1, Maharam Mibrisk 3: 29, Nitei Gavriel ”“ Chanuka 60: 3 et. al.)
Horav Shlomo Miller’s Shlit’a opinion is similar.