Since a large part of marriage is to create legitimate heirs, would peasants get legally/religiously married even though they didn't have anything to inherit? Or was it more of a common law sort of thing, where you didn't do anything officially, but still accept each other as spouses?
First of all, there were many things that could be inherited even if you did not own land.
In England, the son of a tenant farmer had the right to inherit his father's tenancy - as long as he could pay the fees, the landlord did not have the right to replace him.
Even serfs had the right to private property and many would do business on the side and earn money, sometimes to buy themselves free, sometimes to acquire a small amount of luxuries or other things. Tools, clothes, animals (often goats or sheep since they could provide both milk and wool) as well as family heirlooms and Money could be inherited´even by serfs.
In medieval Sweden, all free men, regardless of land ownership status, were required to keep and train with arms. According to the medieval county laws, even sons born out of wedlock had the right to inherit arms and armour (but nothing else).
Marriage created a social structure around the family, with relatives able to help if one of the spouses would take ill or die and were used as such even if there were no land ownership involved.
There are surviving church books with marriages from the 14th century from France and Italy.