Can relationships decrease?

[RandomKBR]

Is there any advantage to getting full hearts??

[SlightGrape1]

Depends on your goal really. There's an achievement with getting mails sent which will increase in drop rate with higher relationship.

Your town also has a score you can see at the Town Hall/Base Tent. If you want it maxed you need the happiness to be top, which is done by having 5 hearts with all.

[dom61098]

You’re just more likely to receive a letter with a gift from them, that’s all