As you can tell, there are lots of citizens in your town. Friendships are very important if you want your town to have lots of citizens or you just don't want people in your village to leave. There are a few easy ways to make friendships:
Sending letters to citizens of the village will make them want to stay in the village. Throwing in an item wont hurt either. But, proper grammar and punctuation are very important. If you send a letter with out proper punctuation, grammar or spelling, you will get a letter back saying that they don't understand your letter and not to send them anymore weird letters.
Doing favors for citizens can help keep them in the village and always has a reward for you. Just talk to a villager and choose the first thing on the list of choices, usually things like: "I need work." or "Need any help?". They will either say they don't need help or that they do, usually the latter. They will tell you to either retrieve something or possibly ask for a piece of foreign fruit. Note: When doing favors, you may have to go to more than one person to get the item you are looking for.
Simply making conversation will definitely keep villagers in the town. To make conversation you must choose the second option on the menu. Not only does this keep citizens around, it can let you in on some interesting insight on their lives.
Don't time travel too far
Time traveling is okay, so long as you don't time travel to much further than a week or so. Villagers will forget who you are and you will have to go through everything you did before to get the friendship back.