batt or alt?

Let me try to explain my situation the best I can.... I own a 2000 silverado.5.3l. I have installed a stereo sony cdx780 head unit, with 4 volt pre out, and a kicker amp ix402. Running 8 gauge wire from the battery to the amp, fused 12" from the battery.Grounded to the chassis 18" fro the amp. Running 2-12" bostons, the amp is bridged. I have a stock battery 600cca and 300 Load test? Stock alt,putting out 105 amps. I am having voltage drops.I can see the voltage gauge in the truck drop and go down. when i leave the truck sit for a long period of time the voltage is up, as i drive and play the stereo it drops low and lights dim. And the amp is unable to get the required current and sounds different. I have done a test on the alt and it is putting out 14.4-14.5, 100% working, now my battery is at 70% not running and drops slowly when the stereo is playing(hard)which it is going to do !. So what do i need to do? I can upgrade the alt to 145 from 105. I am wondering why such the voltage drops?. Could it be that my alt is slipping on the pulley when the load is put on it or when it gets warm would it give out,or is it able to handle the amp draw, or is my battery so low that the alt doesn't have time to replace the used voltage.? What should I do? replace the battery with a new one? and what type, size. And if i just upgrade the alt would it help the battery(stock) that is in it work better? When i decide to do something I will also upgrade the grounds and power wires to better handle the draw from the amp.I am stuck at a spot where i have no idea what to do. I know everything costs money, however I want resolve the problem i am tired of wondering what to do. Does anyone have or had this issue and what resolved it?..