I dont really think carrying weight is much of a problem. After every big quest I deposit all my junk and verify my gear scrapping the ones I will not use. During the quests I just get most of the junk paying special attention to the ones I highlight, and just ignore repeated weapons and standard gears. When I get full I give evetything to my companion.
After getting the "using AP to move fast perk then finally hitting level 30 and picking "encumberment doesn't stop fast travelling" perk, I scavenge modded gear and weapons off murdered raiders and fast travel to my main settlement and unload it all, switch out the good mods with standards, and leave the good mods in the workshop. If you can get them, you will not regret it.