What do you mean by "you'd better to" ? This has no meaning at all - as an expression, it does not exist! Are you thinking of expressions such as "You'd better go" or "You'd better stop"? (without 'to') ? Here's what they mean: "You'd better go." = There is a very good reason why you should go, and there will be negative consequences if you don't go. "You might as well go." = There is no reason why you shouldn't go. It will do no harm for you to go. As you can see, they are different ideas. "You'd better go now" means that there'll be problems if you don't go. If you don't leave now, you'll miss your flight. "You might as well go now" suggests that it'll do no harm to go now - you have no reason not to leave now. You've packed your bags, said your goodbyes, and you've nothing else to do. There's no point hanging around any longer, so why not leave now? I hope that's clear.

This is a different usage of "as well." Here, the word "well" means "good." If something is "just as well," it is "just as good," or equally good. If you say that something is "just as well," it usually means that it isn't what you wanted to happen, but you think it is probably just as good as what you did want. For example: A: "Do you want to see a movie with me tonight?" B: "Sorry, I have to work tonight, so I can't." A: "Oh. That's okay, I have a lot of homework to do, so it's probably just as well." (meaning: it's probably good that you're busy, actually, because otherwise, I would go to a movie instead of doing my homework) "Might as well" and "may as well" are similar to this. "We might as well just leave" means it's probably good to leave, instead of staying. "You may as well buy it, since it's on sale" means that because it's on sale, it's probably good to buy it. The literal meaning is that it's /equally/ good (just "as good") to do it or not do it, which sounds more friendly/casual than saying that we definitely "should" do it. "Since you don't like your job, you should quit." (sounds like the person is telling you what to do) "You might as well quit your job, since you don't like it." (sounds more like a casual suggestion)

"Might as well" is a highly idiomatic phrase. It's usually used when the subject does not want to do something, but has no good reason not to do so. "I might as well take the dog outside when I take out the garbage." It is also used sarcastically to mock someone while implying their idea is bad. A: "I am going to buy seven houses." B: "You might as well buy the whole town!" Note: be very careful when using this phrase sarcastically. In some places, it is very rude to use this with strangers or people you don't know well. But it is appropriate to use if you commonly joke with a particular friend.