How worried should one be about the lay precepts? I took the lay precepts after a short retreat. It was suggested that we say them however loudly we mean them.

I'm kinda worried about this. I may have over-estimated how much I meant them, and also, I may have said them too loudly anyway due to getting caught up in the moment.

This concerns me: what does it mean to break the precepts?
Precept is a promise or pledge or vow to abstain from certain actions. When you break a precept you break the promise, i.e., you pledged you will abstain but you have done what you promised not to do. You should retake the precept, i.e., promise or pledge or vow to abide by the rule of abstaining.

Also saying them loudly maybe you are psychologically more serious about preserving or abiding by them. Also as with any pledge or promise or vow you should mean it and have intention to keep it.

The abstainment in the precepts are towards actions that are unwholesome. So if you break them this also means you are doing something unwholesome hence accumulating bad Kamma. Precepts is a rule base or ritualistic approach from abstaining from what is unwholesome.