Is it normal to like someone !only! because they like me

Being appreciated and liked does actually increase attraction in people with normal self-esteem. But if your self-esteem is compromised then you will definitely be susceptible to liking someone simply because they like you and for no other good reason.

It happened to me when I was clinically depressed. I ended up entangled with someone I wouldn't even have batted an eyelash at had I been in my right mind. But at the time it was nice to be liked when I didn't like myself very much at all.

you seem like you may have low self esteem , could be lonely or have had trouble with finding partners . I also think you might just be really timid , maybe you don't know how to say no ? if you DO actually like them then maybe you are confused on what you actually want so this is easier and keeps you occupied . I think you should give people a fair chance though which seems ironic since you seem to give anyone who likes you a chance but it probably wont last and will hurt them when you realize later you don't actually like them .

Maybe you're codependent, and have low self esteem?

I know how you feel.

When you say like do you mean on a friendship or relationship level? Either way only liking someone because they like you is a bit of a lead on. There is no sense in wasting yours or someone elses time when you don't genuinely like them.

Human beings generally have a desire to be liked by others and hitherto reciprocate that feeling when it is given...but usualy on a platonic level not realy romanticaly.So if you like this person romanticaly then i'd say its a self esteem issue.