OK, I was playing as Cathy, doing very well and heading for a UN diplo victory against Hammarabi. Fred was vassaled to me, and Willem was Friendly with me. He had Artillery and Infantry while I persued the electricity/radio/MM since Cossacks were enough to take care of Hammarabi. As soon as I teched off Assembly line he declares war at Friendly. Has anyone seen him Back-stab at friendly before, or was it an attaempt to hit Fred?

Since Fred was your vassal he took that into account. For example if Willem was cautious to fred and friendly to you, he was (cautious + friendly)/2 = pleased with your team. Willem has a base peaceweight of 4 and 10/50/80/100 peace probability, so there is a decent chance for him to declare at pleased, which is what happened here

Peaceweight has nothing to do with whether they'll attack or not, it just affects AI to AI relations.

the way I understand it, it does only (directly) effect AI relations, but the lower it is, the more aggressive the AI's personality.
If I'm wrong, I'd appreciate it if someone could clarify for me.

Usually, but some civ's peaceweights and aggressiveness don't agree.

Pacal is one of the biggest peacemongers, his aggression is rated as quite low, which puts him in the same league as Elizabeth and Ghandi, but his peaceweight is 2, making him one of the few builders who's not despised by the warmongers.

Qin Shi Huang also has a peaceweight of 2, and unlike Pacal has a warmonger respect of 2, really making him get along with the warmongers, but he's also rated as "quite low" on aggression.

Wang Kon has a peaceweight of 8, but an aggression level of high.

Thanks! The main point though is that the AI combines it's attitude towards you AND your vassals when running it's DoW checks.