Sometimes when the farmer gives a gift to a villager, 3 hearts will appear above their head. This action is known as heart gifting and is the best way to earn affection for the villagers. Below, I will list the known heart gifts through what I have tried.

Terry - Mushrooms

Ronald - grapes

Joe - high quality corn

Ellen - High quality breadfruit, high quality cocoa

Alex - High quality turnips

Saibara - High quality eggplant

Woody - High quality eggplant

Liz - High quality pumpkin

Ray - Moonstone

Louis - Moonstone

Tai - Rare ore

Tim - Pudding

Martha - High quality breadfruit, High quality cocoa

Ann - Corn, rare ore

Mayor Theodore - potatoes

Michael - Potatoes

Doug - corn

Dia - Blueberries

Bob - Silver ore

Basil - Potana root, red herb

Blue - High quality eggplant

Kurt - blue mist flowers

I am aware that there are other villagers, but I have yet to try them all.