I want to hang this pulley system in my garage (partially pictured above) and probably will be loading it up somewhere between 100-200 lbs of plate weights:
What is my best option? Putting a 2x4 across multiple trusses with lag screws and hanging from that? Doubling up some studs and building out some kind of arm support system? Some other option I am not aware of? I am not familiar with how much additional weight (beyond keeping the roof up) either of these two options can support and don’t want to cause any kind of structural damage, to the garage or myself! Thank you.
I'd go with the 4x2, those trusses each look sufficient to hold a 100kg or more,
Spreading the load won't hurt, place the 4x2 above the bottom chord of the trusses and use nails or screws to hold it in place,
The carrying capacity of beams is much stronger right next to a vertical support. So put your pulley as close as possible to the wall, so all the downforce is there. And also use the multiple beam-spanning idea - however that is only as good as the stiffness of your spanners. If you have the height, use a 2x6 on edge.
The roof truss may be stiff, but what keeps the opposite walls from going paralellogram when you put sideload on the ceiling truss? I would run a string diagonally from the bottom of the opposite wall to a little eyebolt "pulley" at the top of this wall, then straight down to a weight. Put a dot with a magic marker on the string. Watch it as you exercise, and see if it moves. If it does, you're tilting the whole building and it's time to stop!