The Federation's first encounter with Weyoun takes place in the fourth season episode "To The Death". At this time, the Vorta's expertise in cloning is not yet known and wouldn't become known until Captain Sisko's first meeting with Weyoun 5.
Weyoun 4 was the leader of a Jem'Hadar unit that co-operated with the crew of the USS Defiant in 2372 to hunt down and eliminate a group of Jem'Hadar that had betrayed the Dominion. These renegades had discovered a device left behind on the planet Vadros IV by the ancient civilisation known as the Iconians, a device that served as a gateway to anywhere in the galaxy. Weyoun's mission was to eliminate the renegade Jem'Hadar and destroy the gateway before it could be used to undermine the Dominion. During the mission, Weyoun's Jem'Hadar and the Defiant crew found it difficult to trust one another, but neither group trusted the devious Vorta.
After the Iconian gateway was destroyed, Weyoun beamed down from the Defiant hoping to inspect the wreckage. The gateway's destruction had lifted a dampening field over the area, allowing the team's phasers to work again. The Jem'Hadar First, Omet'iklan, took the opportunity to dispose of Weyoun and vaporised him.
The fifth incarnation of Weyoun first appeared in the fifth season episode "Ties of Blood and Water". This episode revealed the Vorta's expertise in cloning and Weyoun 5 would live throughout the first year of the Dominion War. His death was never shown on-screen, but in the seventh season episode "Treachery, Faith and the Great River", Weyoun 7 tells Odo that Weyoun 5 was killed in a transporter accident. Damar was supposed to have been on the transporter pad with Weyoun 5 at the time of the accident but was called away at the last minute, leading Weyoun 7 to suspect that Damar was responsible for killing Weyoun 5 as some kind of sick joke.
The sixth Weyoun was considered defective by the Vorta because he questioned the policies of the Dominion. This Weyoun fled from Cardassia and arranged a secret rendezvous with Odo, informing him that he wished to defect and serve only him. He also told Odo that the Founders had been afflicted with a morphogenic virus that had spread across the entire Great Link.
Fearing that Weyoun 6 would divulge the Dominion's secrets to the Federation, Damar and Weyoun 7 dispatched a squad of Jem'Hadar fighters to intercept the Rio Grande. The runabout was cornered inside a Kuiper belt and Weyoun 6 sacrificed himself to save Odo by activating a self-termination implant. With Weyoun 6 dead, Weyoun 7 called off the Jem'Hadar. Though there was a risk that Weyoun 6 may have given sensitive information to Odo, Weyoun 7 was still pathologically loyal to all changelings - Odo included - and would not harm him.
The seventh Weyoun would meet his sudden demise in the episode "Strange Bedfellows". After Worf and Ezri Dax had been captured by the Breen and taken to Cardassia for interrogation and execution, Weyoun gloated over his prisoners' situation, which angered Worf. Worf made a sudden grab for Weyoun and snapped his neck.
The final Weyoun clone. He was activated just hours after the death of Weyoun 7 and he would become the last Weyoun following the destruction of the Vorta cloning facilities by Damar's resistance movement. This final Weyoun would be killed by Elim Garak, who used the deceased Damar's phaser to shoot him after the resistance breached Dominion Headquarters in the DS9 series finale, "What You Leave Behind".