Was a good link. Anyway, here's my word on the matter. Firstly, you want to have good flexibility in both legs. Regardless of whichever side is your lead, a lack of flexibility is going to give you awful posture when performing kicks, and they're therefore going to be less powerful, on top of being less powerful because the capacity of your tendons stretching is reached more quickly, making it hard to get fast acceleration.
Secondly, your dominant side (you never stated if you were right hand or left hand southpaw. I'm going to assume that you're left since your kicks are weaker as southpaw) will always naturally be stronger. You can't help this.
Lastly, it might just be a strength issue. As said above, your natural side is stronger, so maybe it has something to do with being a little too weak to really make them effective. If none of these things are your problems, then it's your execution (form, posture, technique, whatever you want to call it) of the kicks, whether it be lack of proper weight shifting, following through, whatever. Find out what you think you're doing wrong, fix it, and continue practicing kicks until they feel right. If there's more than one problem, then fix one at a time.
