Siman 136

In Gittin (60b) it is explained that after the kohen and levi, the Israelites read, and whoever is prior in status is prior in his ascent to the Torah. And thus our sages, of blessed memory, said: that after the levi, the talmidei chachamim who are appointed over the community read. And after them, talmidei chachamim who are fit to be appointed as leaders over the community, meaning that they ask him a matter of halacha in any place and he says it. And after them, the sons of talmidei chachamim whose fathers are appointed over the community, because of the honor of their fathers. And after that, the heads of the synagogues and all the people. And it appears that since they did not say also "the sons of talmidei chachamim who are fit to be appointed" — we learn from this that for the sake of the honor of the fathers, it is only specifically when they are already appointed. And this is on Shabbat, Yom Tov, Rosh Hashanah, and Yom Kippur.

And it is clear from this that in the essence of the aliyot there is no advantage of one over the other. And now we hold the third and sixth to be the greatest aliyot. And the Ashkenazim hold the third, and the rabbi of the community ascends only for the third if he is not a kohen or a levi. And the Sephardim hold the sixth to be of greater importance, as it is according to the Zohar. And it is understood that it is impossible for us to act according to the law of the Gemara, for we have no parnasim in our many iniquities, and we have no Torah scholar whom they ask a matter of halacha in any place and he says it. And all the more so when they sell the aliyot, whoever buys ascends. And nevertheless, if one buys all the aliyot and honors others—he should see that it be according to the honor, and that there be no disgrace to the Torah. And they honor also the wealthy with the aliyot, because they give income to the beit knesset. And it is a great mitzvah to nullify what is held in the mouths of the masses that this aliyah is very inferior and the like. And whoever is able to conduct himself to ascend to the Torah for the aliyah that they hold to be of inferiority, it is a great mitzvah, for in our many iniquities much dispute comes from this, may Hashem have mercy. And in truth, you have no greater folly than this, for everything is one Torah and one blessing. And this is nothing but the work of the Satan, as it is brought in the Midrash that he only provokes Israel. (See the Magen Avraham who wrote that the leaders of the community precede everyone when there is no exceptionally great Torah scholar there. And for the last one, the greatest of the congregation ascends. And that in a place where they practiced that the parnas ascends—he is not permitted to forgo it for another, see there. And all this is not relevant among us, as is understood. And be precise and you will find it easy.)

Who are the obligated ones, and who takes precedence? There are no laws regarding this from the Gemara or the Rishonim, only from that which has been practiced. The Maharal of Prague instituted that a chatan on the day of his wedding or on the Shabbat after the wedding takes precedence over everyone, and afterwards a bar mitzvah youth, and afterwards the shoshvinim, and afterwards the sandak, and afterwards the mohel, and afterwards the father of the son, and afterwards a yahrzeit (Eliyah Rabbah). And one who marries a virgin takes precedence over one who marries a widow, and a widow over a chalutzah, and a chalutzah over a divorcee (Knesset HaGedolah). And among us there are other customs, and it will be explained in siman 282 (and the Magen Avraham also explained there).