I’ve read that Preston has a carry weight of 165lbs. If I equip him with modified items (such as pocketed armour pieces), will it increase his carry capacity?
According to this wiki page (toward the bottom of the page) companions are affected by pocketed armor.
It is possible to make companions wear pocketed armor to increase their max weight (+30 pounds with basic pockets). There is also a skill magazine perk that will increase the companion carry weight by 10.