The AD&D 2nd Edition Monstrous Manual entry for an Ogre Chieftain says:

He inflicts 8-18 (2d6+6) points of damage per attack, +6 with weapon.

Does this just mean I add another +6 to their damage rolls when they have a weapon? Or does this mean they get weapon damage and then +6? And if it’s the second one, where do I find Ogre sized weapons and stats for those? Or do I just assume human weapon stats?

If armed, roll weapon damage +6

This matches the description of the other ogre varieties e.g.:

1-10 (or by weapon +6)

As well as the section describing the monster attributes at the start of the book:

If the monster uses weapons, the damage done by the typical weapon will be allowed by the parenthetical note "weapon." Damage bonuses due to Strength are listed as a bonus following the damage range.

The equivalent stat block style description for the chieftain would be: "2d6+6 (or by weapon +6)"

Oversized Weapons

Ogres are large and can use large weapons one handed as per the player's handbook:

A character can always wield a weapon equal to his own size or less. Normally this requires only one hand..

They could use giant weapons with two hands if they could attain them.

A character can also use a weapon once size greater than himself although it must be gripped with two hands.

Taking a cue from the fire giant's description, a giant weapon would do double damage to medium or smaller creatures.

A fire giant’s oversized weapons do double normal (man-sized) damage to all opponents, plus the giant’s strength bonus