Once you complete Vol. 3, you will be given several greeting cards that allow you to promise devotion to anyone with max affection (pink circle with five rotating orbs). You can send this to 22 different people and, depending on who you send it to, will get a "marriage" cutscene followed by ending credits. You can marry any of the females (except Natsume) and Endrance (as the males will just give you a "bro" like ending). If you hold on to one card, you will get another address in Vol. 4.
If you need to max affection for a particular individual, wait until the end as you will also obtain a 3rd Area Keyword: BBQ Plate. In areas formed with this keyword, God Chim Chims will be loafing around much like Un/lucky Animals, waiting to be kicked. It will take 10 hits to fell him, and once you do so, he will increase the affection of both members in your party.