Does Weaponmaster only work when my unit is played, not after two turns?

Yes, Weaponmaster only works when you play the unit. It does not stay in effect to allow you to equip gear at a discount after the unit is already on the board.

According to Rule 821.1.b and Rule 821.2:

• Weaponmaster is a Play Effect: The keyword functions specifically as a triggered ability that triggers "When you play me."
• Inactive on Board: Once the unit with Weaponmaster has finished entering the board, the keyword becomes inactive and has no further function (Rule 821.2).

As clarified in RiftJudge FAQ #10048 and FAQ #9161, this is a one-time opportunity that occurs exclusively as part of the process of playing the unit. Once the unit is on the battlefield—even just one turn later—you cannot use the Weaponmaster ability to equip gear. Any subsequent equipping must be done according to the standard rules for the Equip keyword (paying the full cost during your Main Phase when the chain is empty).