Ah, I know with almost
complete certainty what this is!
I've been collecting examples of the fearsome lead-weighted
Roman Plumbata dart/javelin for years, and your item appears to be the point of just such a dart. There were of course variations in
style through time and across the empire but the general rule was that the tip
had a square/diamond cross-section and 2 barbs. Attached is a pic of some of my examples, plus a similar loose broken plumbata tip.