My goal.

[AceInfinity]

It'll be difficult to hit your back and chest hard without some heavier weights.

There's lots of exercises for your chest and back, you don't need heavier weights to rely on. If you rely on that for getting bigger in areas like that, you'll only end up doing exercises improperly because you won't be focused on technique when lifting them or doing whatever you're doing with those weights. Like any mass building though you need heavy weights anyway.