Montaigne argues a few different things about custom. Firstly, he suggests that custom is very strong. He tells a story about a woman who carried a calf every day. This continued as the calf grew up so eventually she could carry the full grown cow. The sheer repetition of custom is part of its strength.
Secondly he says that we become so used to various customs that they become second nature to us. Many of them are followed without any conscious thought. Customs may look strange from the outside but they almost never do to the practitioners.
Next he says that customs are imprinted on us at a very young age. Montaigne says that parents should be careful about what customs and habits their children are being taught. He speaks of a very strong personal sense of fair play and says that it has been with him since childhood at least.
Montaigne then follows with a very lengthy list of customs from other parts of the world. All of these seem strange to his audience (and they're certainly not common to us). All of these customs seem natural and right to the people who have them.
Fifthly he argues that people accept custom while rarely if ever thinking through the reasons behind those customs. He adds to this point by saying that even when custom is superseded by law, it remains strong.
The next point he makes is that it is difficult and dangerous to try and change an established custom. Customs (and laws) are interconnected and the whole structure resists changes to parts of it. This is an outstanding point and one that is poorly understood even today.
Montaigne says that he, himself, dislikes novelty. He goes on to speak of the danger of change:
They who give the first shock to a state, are almost naturally the first overwhelmed in its ruin; the fruits of public commotion are seldom enjoyed by him who was the first motor; he beats and disturbs the water for another's net.He urges extreme caution on those who would try to change customs:
. . . for whoesever shall take upon him to chose and alter . . . should look well about him, and make it his business to discern clearly the defect of what he would abolish, and the virtue of what he is about to introduce.The idea that custom is a mere custom is fairly commonplace today. Large sections of behavior are dismissed as merely being the things that people do. Comparatively, very little thought is given to what happens when that behavior is changed.
In some ways this reminds me of the debates surrounding gay marriage. (Full disclosure, I'm a supporter.) As little as thirty years ago, the idea of gay marriage was somewhat ridiculous, even to gay couples. Now there are large pockets of opinion that hold that opposition must be due to bigotry. How much work have supporters done to think about possible defects?
Montaigne does a very thorough job of looking at how custom is created and how it should be regarded. I'd highly recommend this essay.