The image of a heavy rock falling through a fragile spider web helps convey the vulnerability of humanity's position in relation to God's power.
The main thesis of "Sinners in the Hands of an Angry God" is that the congregation members should repent of their sinful lifestyle, or they will go to hell. The sinners are the spiders, and their artificial righteousness is the cobweb. Jonathan Edwards is saying that just like the spider's web won't be strong enough to stop a rock from falling through it, his audience's prayers and small efforts won't be enough to protect them from hell fire unless they seek forgiveness and change their ways.
