Before the creation of the professional army, a Roman citizen would keep a weapon in his home because he was expected to. The armed forces of Rome consisted of citizens called up to fight with whatever equipment they possessed. The rich could afford to buy themselves nice armour, a shield, sword, and spear or throwing spears; poorer citizens might only have a few of these items, or, if they could not afford a sword or spear, they would arm themselves with javelins or a simple sling. In peacetime these things would of course be kept around the house.

To my knowledge, though, there is no reference in any ancient source to the threat of home invasion that is often used nowadays as a justification for keeping weapons in the house. It doesn't seem to have been something people were very worried about. Even in wartime, the common response to the threat of invasion was to seek refuge in a city or stronghold, rather than to stock up on weapons in one's own property. (I would be happy to be corrected on this by someone more familiar with the Roman material.)