I am a fabricator. Tough problem. If the countertop was properly installed there is no mechanical stress on the granite and no reason for it to crack so the too tight faucet nut is at least possible. I would look along the underside of the countertop to see if it is shimmed so that every part has support. Typically the tops of the cabinetry are not perfectly level and the underside of the stone is also not perfectly flat so some shimming is required. if some section is not supported then a crack developing is quite possible. However, since granite has a compressive strength similar to concrete it's difficult to imagine tightening a faucet nut enough to harm the granite. In fact, it seems impossible to me. unless you can determine that the tops were improperly installed your best bet is to let the fabricator repair the crack. A well done repair will make the crack invisible or nearly so. you might ask the fabricator if the sink area is "rodded". Rodding is the technique used to strengthen the rails around the sink by glueing in a steel or fiberglass rod in the underside of the rail. the rod prevents movement much like rebar in concrete in the event a crack develops. A repair of the crack is much more likely to be permenant if the stone is rodded.

Your fabricator really should address this for you.... Barring that, you could do it yourself using epoxy (it's not too difficult to use) or even superglue. I've filled in a few chips this way. You would fill in with the epoxy/superglue, scrape away excess with the side/edge of a razor blade, and then "buff" with fine steel wool. Usually it'll start out dull, but eventually becomes less so as I continue to buff. I also dab a little sealer on it to bring up the shine (the stuff our fabricator used adds shine, too, as it is a polish/sealer???). If the fissure isn't deep enough, the glue might not stay--I think it needs something to adhere to (eg. unpolished stone edges), but might be worth a try if your guy won't do it.

No probably not, but they might consider fixing it. The top guy is going to blame the cabinet guy, and the cabinet guy is going to blame the top buy, and the builder is (has) told you the house had a 1 year warranty. The subs (cabinet/top guys) have to warranty a year (hence how the build warranties it). I would try the original installer/fab shop, if you talk calm and non-threatening they might come look at it, and offer to fix (or discount the fix). Of course, this depends on the reputation of the sub the builder hired in the first place. If it was my job, I would at least come look at it, and try to find the reason for the crack. Whether it is a quality/workmanship issue, or a damage/abuse issue. Depending on what I found, and the attitudes of those involved, I could be moved to either fix it, discount the fix, or nothing. In your case, you have nothing to lose by being nice and calm, and asking for a fair solution.

I just noticed the crack spans a cooktop cutout. If so, it could be a blown reinforcement rod. Look up under the overhang please. You may see a line about 1/4" thick filled with resin. If so your top is rodded. Just because you don't see the line doesn't mean the top isn't rodded; you may have to pop off the cabinet front to see. Ask your fabricator if he rodded the top.