We find in several contexts the concept of ma’alin bakodesh v’ein moridin[1] – one may only raise the status of a sacred object (or person) but not diminish it. The question is thus if this principle is relevant to your case regarding the Shabbat tallit.
The Beit Yosef[2] cites the Mordechai,[3] who says that an object that was used for the purposes of a mitzva, such as a candelabrum in shul, may be switched to another mitzva use, even if the latter is of a lower level of importance than the former. He explains that ma’alin bakodesh v’ein moridin applies to tashmishei kedusha (objects that “serve holiness,” especially sacred scrolls), but not to tashmishei mitzva (objects that are not holy, even though they are used for mitzvot). Some Acharonim[4] posit that since tzitzit is a classic tashmish mitzva,[5] ma’alin bakodesh v’ein moridin does not apply to it; one may switch it to another mitzva use and need only avoid disgracing it.[6] However, these Acharonim do note that there are important sources that apply the principle of ma’alin bakodesh v’ein moridin to tzitzit as well. Those sources may argue with the Mordechai[7] or may represent practices of extra stringency.[8]
The Shulchan Aruch[9] rules that one may remove kosher tzitzit from his garment as long as he will put it on another one. In addition, most Acharonim[10] permit moving the tzitzit from a tallit gadol (what we call a tallit) to a tallit katan (what we call tzitzit). However, there is a minority opinion that does forbid doing so, invoking the concept of ma’alin bakodesh v’ein moridin, as based on halachic or Kabbalistic factors, a tallit is of a higher level than tzitzit.[11] Furthermore, not all proponents of the majority opinion dismiss the relevance of ma’alin bakodesh v’ein moridin to a tallit or tzitzit; some agree that it is relevant but deny that there is a fundamental difference between the two garments regarding the mitzva. Moreover, the Magen Avraham[12] and the Mishna Berura[13] explain the minhag of having an atara[14] on the tallit as aiding one to keep the two front tzitzit in their more prominent position, the importance of which is due to the principle of ma’alin bakodesh v’ein moridin. While they note that the Ari’s practice was not to be careful to maintain the positions of the tallit’s sides, the stringent opinion that one should be careful appears to be quite accepted. Thus, we see that it is not always obvious how to determine when a change to a tallit is a prohibited diminishment. It is therefore worthwhile to seek additional grounds for leniency.
The Taz[15] suggests that if one has decided to stop using a holy object for its designated purpose, making it a candidate for geniza, it is better to “lower” its usage than to totally take it out of use. Based on this, since it is appropriate to periodically upgrade a Shabbat tallit, it actually would be preferable to use the old Shabbat tallit during the week, rather than to stop using it completely. However, the Taz’s opinion is not widely accepted.[16]
One strategy that might prevent your question from being a real issue is to stipulate, when you initially purchase the tallit, your intention to eventually transfer it to weekday use.[17] However, usage of the idea of stipulations in such matters is not a simple matter.[18]
Despite scant authoritative discussion of the topic, we would confidently permit one to transfer a tallit from Shabbat use to weekday use for the following reasons: It is unclear to begin with that a Shabbat tallit has any more mitzva importance than a weekday one does. First, the fact that the weekday tallit is used six days a week as opposed to only once may have halachic significance and actually give the weekday tallit more mitzva-importance. More fundamentally, even if a Shabbat tallit is more prominent than a weekday one, this is not in regard to the mitzva of tzitzit but rather because wearing nicer garments is a means of honoring Shabbat.[19] Therefore, one could claim that buying a new tallit and using the old one for weekdays is comparable to buying a new suit for Shabbat and using the old one for weekdays – a practice we have never heard questioned on the grounds of ma’alin bakodesh v’ein moridin.
Thus, based on several reasons, one should have no compunctions about using a former Shabbat tallit for weekdays.