The enlarge happens only at casting time.
Both spells explicitly state that "Any [enlarged, reduced] item that leaves an [enlarged, reduced] creature's possession (including a projectile or thrown weapon) instantly returns to its normal size." Since they don't mention any size change when entering such a creature's possession, it's safe to assume they intentionally didn't include it because they didn't intend it to happen.
Game balance explanation
Essentially you have covered the reasons why this is the way the spells ought to work for balance purposes. A lot of funky behavior is possible when items are enlargeable; however, enlarging a person is far less useful if you can't enlarge their weapons, clothing, and armor, as well. Presumably, instead of drawing the line at "worn or held", and having the tricky "backpack grows, contents don't" situation, they include everything carried and not just held.
Game physics explanation
For a "realistic" justification of this behavior, think of it as a magic field initially shrink-wrapping the creature and its possessions, enchanting it, and then dissipating. When an item exits the shrink-wrapped area, it returns to its mundane size and the shrink-wrap shrinks to its new shape. Picking up an ally, then, won't add the ally or his gear to the shrink-wrap.