tosafos on 113a says that based on the mishnah that says that there are limitations on folding one's clothing on shabbos, one should not fold his tallis on shabbos since this it Tzorech Machar. What are some of the reasons why one does not fold his tallis on shabbos and what is the established halachah?
As you correctly pointed out, one reason for the prohibition of folding clothes on Shabbos, is because it is Tzorech Machar, and indeed, it is never permitted to fold one's Talis on Shabbos for tomorrow in its regular folds. The Bi'urei ha'Daf cites the Levush, who permits folding one's Tallis on Shabbos not in its regular folds, and the Mishnah B'rurah explains that this applies even if he has no intention of wearing it again on Shabbos. The Poskim say however, that this is only if one goes on to re-fold it properly after Shabbos (which is anyway advisable as it is a Segulah for Shalom Bayis). But if one intends to leave it as it is (and the example for this he gives as someone who is folding his Shabbos Tallis which will remain folded in this way until the following Shabbos), then even folding it not in its folds is forbidden.
The Mishna B'rurah does conclude though that if one does not care how one folds it, and does so one week this way, and the next week, another way, it is permitted.
It is also clear from the Gemara that there is an additional Isur in folding clothes in a professional way, as it removes unwanted creases, and entails an Isur mi'de'Rabbanan of Tikun Mana.
That is why the Gemara forbids folding clothes even if one intends to wear them on the same day, unless the four conditions mentioned in the Sugya are met. And in this connection too, the Shulchan Aruch (Siman 302:3) permits it as long as one does not fold them in their original folds.