Why were the Triarii differently equipped?

[Urselius]

The Romans were always sensitive about arms (weapons) in the hands of citizens. People in towns and cities were not usually allowed to bear arms - rioters armed with spears and swords would be far more dangerous than those armed with staves and knives. A parallel can be seen in Tudor England where arms were usually kept in Parish churches, to be issued to militia (Trained Bands) for training and in time of emergency. There may well have been a different system for arms storage and issue than that for defensive equipment (armour) in early Rome.

Before anyone cries out "Where are your primary sources for this?" I'm a scientist and I am quite happy to deal in theories, if definitive proof is absent.