Was looking at the stats on the Psi-blade and had some thoughts.
1} the weapon attributes (other than 'Psi' trait) are exactly the same as a similar non-'Psi' melee weapon; so maybe make 'Psi' a trait that can apply to any melee weapon.
2} the weapon gets adds to 'Damage' and 'Armor Penetration' based on the Psi attribute DM, and that seems a little wonky.
Psi is one of the attributes which can fluctuate from round to round (and even action to action) and some wielders might have a negative DM to start with. Adding a skill level (like Clairvoyance or Telekinesis) seems like a less confusing way to handle this. Also, with melee weapons 'Effect' adds directly to damage. So my suggestion for the 'Psi' trait:
Psi weapon: A user has a bonus to hit (and/or to parry) equal to one plus their skill level in the Clairvoyance talent, and an Armor Penetration of 1 plus 5x their skill level in the Telekinesis talent. A wielder may expend Psi strength at any time to increase these boni with the weapon as though their skill with all the appropriate talents was one higher per Psi strength point spent; these boni last until the end of the wielder's next turn. A weilder who makes a successful use of the 'Tactical Awareness' task may apply the weapons bonus to parrying (only) against all incoming attacks (without needing to take the 'parry' action) for as long as 'Tactical Awareness' lasts; taking the 'Parry' action allows the user to use their full skill plus the weapon's bonus against all incoming attacks for as long as 'Tactical Awareness' lasts.
Edit: Also -- many (especially melee) weapons seem very heavy; maybe tone some of these down? Listing the weights in grams instead of kg might help.