If I use the spell enlarge, and then hold a large weapon, how does it affect the damage? (I mean use enlarge and then hold a large weapon off the ground).

I read the spell (reduce / enlarge) but it only talks about modified damage for weapons that you currently hold or have in your possession, but not for weapons that you could hold that are large and that you currently qualify to use. (Or for at least I didn't understand that point)

Just to clarify your question.  I assume you are asking if a medium sized PC is enlarged to a large creature can he pick up an Ogre's great club and do the 2d8 damage from the Ogre stat block?

I believe the answer is "no".  In the PC hand's it will do base1d8 of a great club plus the extra 1d4 from the spell.

I imagined it, and if I meant exactly that kind of situation. Thank you very much for the clarification.

When you cast enlarge/reduce it also includes your equipment, which is what gives you the extra damage.  Picking up a weapon after being enlarged does not confer the bonus 1d4 damage.

The target's weapons also grow to match its new size. While these weapons are enlarged, the target's attacks with them deal 1d4 extra damage.