| Gitin
"These are the things that are said mipnei darchei shalom." (Gittin 59) After listing a series of rabbinic enactments mipnei tikkun olam,for the betterment of the world, the Mishna lists a series of laws instituted mipnei darchei shalom, in order to promote peace. While promoting peace surely falls under the rubric of making the world a better place the enactments mipnei tikkun olam focus on broad social issues whereas those mipnei darchei shalom focus more on preventing actual strife between people. Thus overpaying for hostages, allowing people to collect loans after a shmita year, ensuring slaves can marry and not overpaying for religious articles fall under the rubric of tikkun olam. The takkanot instituted mipnei darchei shalom are much more localized and begin with the obligation of giving the first aliyah to the kohen. 
As honouring kohanim is rooted in Biblical text there seems to be little reason for a special decree to ensure the kohen gets the first aliyah. The rabbinic enactment of darchei shalom adds that the kohen may not waive the right to the first aliyah by letting someone else have that honour. 
Jewish law allows a parent or Torah scholar to waive the honour due them and because of the difficulty of fully and properly honouring parents (Kiddushin 32a)[1]. Jewish tradition actually recommends a parent waive the honour due them. And there should be no reason for a kohen who so desires to refrain from waiving the honour due him. However unlike a teacher-student relationship and even more so a child parent relationship where the honour is of a more subjective and private nature, a kohen waiving his right to the first aliyah is a clear public display of mechilah, waiving of honour. In and of itself there is nothing wrong with that except that what happens when one Monday morning the kohen is not mochel his aliyah? "How come you did it for him but not for me" a disgruntled shul goer might say. Being mochel on occasion is a recipe for disaster. And in order to ensure such does not happen the rabbis ruled that a kohen may never waive his aliyah
However the Gemara goes on to say that this only applies on Shabbat when there are lots of people in shul. But on a Monday or Thursday when attendance is sparse and presumably the camaraderie amongst the few who go to shul high, there is little concern if the kohen wants to given his aliyah to someone else[2]. And thus Tosafot notes that this exception to the rule no longer applies. Nidgadlu hadorot, apparently the people had become greater and more pious than those of the Talmudic era "who during the week were busy with their work and were not commonly [in shul] but by us they are as crowded on Monday and Thursday just like on Yom Tov." (Tosafot 59b s.v. Aval)
I find this comment (taking up 3 small lines) of Tosafot fascinating. Did people work less during the time of Tosafists - at least where the author of this Tosafist [3] lived - or did they go to shul during the week despite their busy work schedule? The Gemara in Brachot notes that workers (at least in Talmudic times) had to shorten their prayers lest they take too much time from work. And considering they davened on the job - with work beginning at day break they had little choice - they were not attending morning services. Might the fact that many Jews - due to laws forbidding Jews in many trades - were self-employed been the catalyst for increased numbers in shul?
In any event changing circumstances meant no longer could a kohen be allowed to waive his aliyah on Mondays and Thursdays[4]. Yet circumstances continually evolve. Rav Soloveitchik and others have notedthat we today may observe the original law of the Gemara. With shul attendance much higher on Shabbat than on weekdays kohanim may once again waive their aliyot on Mondays and Thursdays.  
[1] The Talmud relates that Rabbi Tarfon used to wait by his mother's bed so that when she awoke she could put her feet in his hand and not on the cold floor. When he "bragged" in the beit midrash about how meticulously he observed the mitzva of kivud eim his colleagues responded "you have not even reached half the honour due to your mother." (Kiddushin 31b)
[2] I might also suggest that people just don't have the time or energy to argue during the weekday minyanim. People are rushing off to work and the arguments can wait until the relaxed davening of a long Shabbat morning. 
[3] This comment is quoted in the name of "Rach" (Reish Chet) and I am at a loss as to exactly who this is referring to. For historical reasons it would be instructive to know if this might be Rabbeinu Chananel, Rabbeinu Chaim or one of the many other Tosafists whose name starts with a "chet".
[4] Yet one Tosafost does not a period make. If we recall that the Tosafists flourished from the 12-14th century in both France and Germany we shall not be surprised to read of the Tosafists lamenting laxity in mitzva observance, including some as basic to a religious Jew as tefillin.