How Do They Do That?
We've looked at why, but what about how? Adventurers tend to be heavily armoured and armed. Their ability to perform acts of violence is well known and well documented. But what about the average people? Their equipment can hardly compare with someone who commits armed robbery for a living!
Improvised Weapons
There are limits as to what sort of weapons peasants are allowed to carry. Most lords don't like the idea of their courtiers walking around with swords, let alone their serfs! Items obviously designed for use as weapons are forbidden by law. If a peasant gets his hands on a spear, mace or even a sword, it's only during wartime and because his lord has issued him with it. He's probably had to sign or at least make his mark on a piece of paper in order to receive it.
Luckily there are plenty of tools that can be used as weapons, and the peasant knows it. Axes, pickaxes, adzes, scythes, sickles, hammers: lots of tools involve the transfer of physical force, and lots of them can be adapted. Knives are always available. Cleavers can be tied to sticks to make polearms, and improvised clubs can be made from almost anything.
Illegal Weapons
Just because a peasant might not be allowed to bear arms legally doesn't mean that he or she has no chance of having one. The only real barriers between peasants and swords are his own fear of being caught out, and the extortionate price they carry: ten gold coins or what have you is usually far beyond what a peasant might make in a month, let alone have as loose change.
Even so, weapons have a way of getting where they shouldn't be. They could be stolen from other people; traded at the bar in return for a few rounds of drinks; or even left behind by careless adventurers or soldiers. Admittedly most serfs wouldn't know how to wield a sword, but they could still wave it around in a threatening way.
Legal Weapons
Even with loads of restrictions on what peasants are allowed to wear and carry, there are still a few items peasants can carry without arousing suspicion. Quarterstaves and clubs are common; pretty much everyone knows how to hit someone else with a stick.
Ranged weapons aren't beyond the peasant's reach either. Slings, shortbows and even javelins and darts might be used when hunting. If the peasants have hunting rights within the nearby forest, then they'll almost certainly access to some kind of ranged weapon, as nobody in their right mind would want to fight a wild boar in mêlée combat!
Better yet, Englishmen were once required by law to practise with a longbow. If you want to make the adventurers' lives difficult, one of the best ways to do that is with a few dozen trained archers! With a few lucky die rolls, the heroes could be reduced to pincushions scant seconds after they've cleared their scabbards!