Everyone is right on, especially about trying to determine where the buzz is coming from. An old mechanics trick is to use a stethescope with a small metal tube on the end instead of that cold round thing. It really allows you to zero in on the source.
It could just be the higher G frequency causing a buzz from something that is loose like a tuning key back cover, the fret itself, or a cracked nut (I hate it when that happens!), something loose inside the body, etc. Tune it higher and see if the buzz changes. If it doesn't, it is probably isolated to that string.
Next string change, get a small mirror and light to inspect the body cavity for loose pieces of wood, braces, etc. Also check for broken string ends that were left behind from a previous string break. They can stick to the inside of the body where the string comes through the bridge.
Inspect the frets closely. Don't just focus on the third fret either. Inspect the fourth fret (and even higher) to be sure they are all seated completely and not broken. If they look good, a straight edge can reveal if some of the frets just need to be leveled and re-crowned.
I once thought a "Sweeping Arpeggio" was an Italian janitor.