Final answer:
Bill Weasley used the codename 'Rapier' on the radio show Potterwatch, which was an underground broadcast sharing real news during Voldemort's control over the wizarding media.
Step-by-step explanation:
The Weasley who was known by the codename 'Rapier' on the Potterwatch radio show was none other than Bill Weasley. Potterwatch was an underground radio program that broadcast news about the wizarding world during the events of the Second Wizarding War, specifically when the mainstream media was under the control of Voldemort and his followers. While most of the Weasley family was involved in the resistance against Voldemort in some capacity, it was Bill who used the alias 'Rapier' while contributing to this radio show.