Well there's a difference between getting invested quickly because of great chemistry and compatibility or getting invested quickly because of neediness.
If you're meeting girls and you have all this great chemistry and compatibility with them then I don't think it's an issue. If you're in this situation then most likely they're equally into you, and you should be able to tell this is the case.
On the other hand, if you're constantly getting into situations where you're really invested in the girl but she doesn't seem as into you, e.g. you want to spend time with her constantly but she doesn't seem to have much time for you, then it's likely coming from a place of neediness.
As you said, it seems to be the latter. So there's a couple of things you can do in this situation:
1) As you begin to date her, continue to spend time on all the things you did before you met her; your friends, your hobbies, work, etc. Don't let her take over all your time.
2) Ask yourself why she's suddenly so important to you and your life. How would you take it if she broke up with you tomorrow? How long would it take for you to get over her? Would you blame yourself and be angry at yourself? Or would you get angry at her and think negative thoughts about her? Basically you want to find out what needs you're trying to fulfill by letting her become important to you so quickly. Maybe you feel you're not very lovable, and you want to hold onto anyone you can get once they show interest. Or maybe you don't have any other close relationships in your life, and you're desperately craving intimacy.
3) Read these articles, which tie in with that last point: http://postmasculine.com/attachment-theory, http://postmasculine.com/emotional-needs-part-1, http://postmasculine.com/emotional-needs-part-2, http://postmasculine.com/emotional-needs-part-3
The first one is especially relevant.
I had/have this specific issue of investing too much, too early in relationships myself, and I've started to narrow it down to a few things. Firstly, I love intimacy and trust in a relationship, so I have very little hesitancy in trying to achieve this as quickly as possible. In my mind this isn't a problem and it's not something I'm looking to change. Secondly, I haven't had a relationship in a while, and I miss the intimacy from it, so I am often overly keen in finding it, which becomes unhealthy when I invest in a girl who hasn't done enough to warrant it yet. That's an issue I'm working on. Thirdly, I'm a strongly attachment type, which means I don't deal well with being single and I need constant reassurance and affection from a girlfriend. This ruined a relationship for me, and it causes me to over-invest in a very unhealthy way. This is something I've been (consciously and unconsciously) working on for the last few years, and it's something I have a way to go with. I'm doing this by being more aware of my motivations when I start to develop investment, and by looking back through my history to see why I don't feel secure even when my needs are being met.
Your challenge is to do the same, and then work with the results.