So it seems that the higher I sing, the more power there is in my voice. Which really bothers me, because for lower songs I have to raise the singing an octave just to get the needed power, but I end up not being able to hit all of the notes in most cases.

Is this natural? Or is there something I can do to work on getting power in the lower registers? I've been practicing but it ends up sounding weak and boring.
Logically speaking it just sounds to me as if you just have a different vocal range than the low voice you're going for.

I wimp out on power in the lower notes as well.. it really bugged me but after working with my singing teacher for a bit she told me I was a soprano.. so I just have to accept that I'm not going to ever really hit those low notes I was trying for. Not to say that you shouldn't work on extending your range (because with a bit of work you CAN), but you'll never go from being a tenor to a bass.

You can keep practicing, but it may just be you have a higher vocal range than what you're going for. As long as you aren't straining your voice or hurting yourself, there's no harm in practicing to hit the lower notes.
A higher vocal range is nothing to be sad about, believe me.

But yes, there are biological limits on how high and low you can sing. So, really, learn to be glad with what you have, because it won't change that much.