This guide will teach you how and when you can marry a character in Fire Emblem Engage. It also details the benefits of marriage in the game.
If you do not see the character you wish to marry, go back upstairs to your room and sleep in your bed. It should reset the character availability in Somniel. Keep doing this if you do not see them.
Marrying a character in Fire Emblem Engage raises the level 20 cap on their bond level. It also adds new bond effects for the character. For example, the character was given the Boon of Elyos effect, which grants Critical Hit and Dodge bonuses equal to 2x the number of allies who acted in the turn when initiating combat.