You do not need to upgrade your PSU. CX 430 is a very decent unit from Corsair, it's a quality power supply. Furthermore, HD 7850 has one 6-pin connector requires, and that's exactly what CX 430 power supply has. It will be easily enough.
Secondly, i3 2100 will not bottleneck any GPU unless you're play on very low resolution (like 800x600). It's a very powerful processor with hyperthreading technology.
Lastly, I do not think you will be able to max out Battlefield 3 with HD 7850 - though if you reduce anti aliasing setting, you will get away with everything else on ultra. Check this:
As you can see, HD 7850 gets an average of 40 fps. That sounds playable, doesn't it? Yes it does! However:
1. It's single player score, so in multiplayer it will be a little bit lower;
2. It's an average score, which means minimum frames per second will be lower in intense action/shooting.
Considered that, it might drop to around 25, which feels very laggy. That's the reason I'd suggest reduce anti aliasing, it will almost double your fps.