Shortly after breaking up with my boyfriend of 7 years I started going out with a guy that I was really crazy about. But I was very insecure and jealous and not sure whether he was really into me as much as I was into him. So I dumped him after 3 months, telling him that I felt it was too soon since my last relationship ended and I wasn't ready for another one.

So on the one hand you thought he wasn't into you as much as you were into him, yet you gave him a completely different story and told him you weren't over your last relationship as the reason you wanted to split up.  Why not just tell him the truth?  Then he might have given you the truth about whether you were right.

I regretted my decision straight away as I do still want him! But I decided if he really wanted me he would contact me and so I left the ball in his court. 

Big mistake, you were the one that made the decision, as far as he is concerned if he approaches you, he's not going to be successful.  For a guy, if there's a good chance he's not going to be successful, then he won't bother.  It would be like humiliation and begging if he pleaded with you and would make him look stupid and put off other women, if they found out.  This indeciseveness will put him off having a long term relationship with you, because he might waste another 3 months of his life going out with you again, only for you to say again that things are not working.  A man doesn't particularly like being messed about.  If he was upset about the split up the best way for him to recover would be to avoid you and find someone else.

If a guy wants out of a relationship, he prefers the woman to finish it, he will sabotage the relationship to make her finish him.  If a guy wants the relationship to continue, he hates it when a woman finishes him, it does upset him although not all guys will show it.

3 weeks later he hasn't contacted me. 

Not surprising, he's not going out with you anymore, he's probably trying to find an alternative, if he hasn't found one already. 

My friends say they are sure he really liked me and that if I want him back I should let him know... 

Yes you should, if you don't let him know, he's not going to guess.

But if I let him know how I feel maybe he will just come back to me because he thinks he can get sex from me,

Yes, that's true, but you could work your way back into his life slowly.  By just starting off as friends, if he'll even consider that.  Gradually build up and let him know you are interested in him again.  That way you give him the message, gently and gradually, instead of either shocking him or making him think, yes, now I'll just use her for sex, then ditch her, like she ditched me. 

then I still won't know if he really likes me and wants to be with me.  What I want to know is, do you think if he really, really liked me he would have contacted me after I dumped him and try to win me back? 

No, as I said above he could have grovelled with you, but that would be humiliating and men don't like to be defeated.  The fact that you ditched him in the first place would have dented his self confidence, he wouldn't have wanted to go through anymore trauma of begging you, because he would have feared you would put the boot into him even more when he was at rock bottom.

Or would he expect me to make the first move since I was the one who ended it?

He would expect you to make the first move, seem as though you finished the relationship with him.  I can't tell you whether he really fancied you or not.  What I can say is the best option available to you, is to try and get him back in your life as a friend initially and break him in gently to the idea of getting back with you.  It maybe a case of he has moved on now and may even have found another girlfriend.  But if you really like him, you are not going to find out unless you try.

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