Dunno how to exploit his weaknesses, I'm such a noob myself. But you can play on your strengths - use phase gates etc - and eliminate his advantages, eg. do hit-and-run raids and break his trade lines. A collapsing economy should be bad in the late game when 60% of your income goes to the fleet upkeep already.

Eat up his undefended planets  with the hit an run tactics. After that you only need to hurt him in each battle. After a while his forces will become very weak quickly, but remember you must cut off the head first.

Economically, make sure you take and hold onto neutral extractors so you can negate his economical advantage and deny him metal/crystal.

Militarily, like others have said, use guerilla tactics (Antorak Marauder works quite well for this purpose) and upgrade your phase missile's ability to bypass shields. Although the shield bypass works less effectively on TEC than Advent (due to their emphasis on hull and armor), skipping the shield is still gives you a big advantage in that your friend would have to go through shields and hull entirely.