Weug was born in Benissa, Costa Blanca, Spain to a Dutch father and a Belgian mother, and has competed under all three national flags across her career. She speaks English, Dutch, Spanish, Catalan (Valencian), and Italian. She began karting at age seven, competing in multiple national championships including the Spanish Karting Championship, where she finished second in the Alevin Class in 2015. In 2016 she stepped onto the international karting stage, winning the WSK Final Cup in the 60 Mini category ahead of future Ferrari Driver Academy member Dino Beganovic.
In October 2020, Weug was nominated as one of twenty female drivers aged between 12 and 16 for the FIA Girls on Track – Rising Stars programme. She progressed to the final selection alongside Doriane Pin, Julia Ayoub, and Antonella Bassani. On 22 January 2021, it was announced that Weug had won the shootout and would join the Ferrari Driver Academy — the first female driver to do so.
Weug made her Formula 4 debut in 2021 in Italian F4 with Iron Lynx Motorsport Lab as part of the Iron Dames programme. She scored three rookie podiums at Le Castellet, Misano, and Vallelunga but did not score main championship points, finishing 35th overall. She was also selected for a one-day FIA Formula 3 test at Magny-Cours in November 2021, alongside Doriane Pin and W Series drivers Nerea Martí and Irina Sidorkova.
In 2022, Weug returned to Italian F4 with Iron Dames partnering Ivan Domingues. A mixed-weather qualifying session at the opening Imola round enabled her to start third and score her first championship point. She went on to record top-ten finishes at Misano, Spa-Francorchamps, and Vallelunga, and finished the season fourteenth in the standings.
Weug progressed to the Formula Regional European Championship in 2023 with KIC Motorsport. Her best result was a rookie win and sixth-place overall finish in the second race at Spa-Francorchamps. She was the only KIC Motorsport driver to score points during the season, accumulating 27 points across six top-ten finishes, ending the year seventeenth overall and third among rookies in a 42-driver field. She made a return appearance in 2024 at the Mugello round again with KIC Motorsport, and in 2025 appeared as a replacement driver with Saintéloc Racing during the fourth round.
Weug moved to F1 Academy for the 2024 season with Prema Racing, representing Scuderia Ferrari. She claimed her maiden race win in Race 3 at Abu Dhabi and recorded a total of one win and eight podiums, finishing third in the championship. Retaining her Ferrari backing for 2025, she switched to MP Motorsport. She won three times — in Race 2 at Jeddah, Race 2 at Zandvoort (her home race), and Race 2 at Singapore — and secured nine podiums across the season. Weug and Doriane Pin were the two main championship contenders heading into the Las Vegas finale, the first time the F1 Academy title had been decided at the final race. Pin took the championship; Weug finished second overall.
For her runner-up result in 2025, Weug received the opportunity to test a Ferrari 296 GT3 with AF Corse on 8 December 2025, fully funded by F1 Academy.
Weug's historic entry into the Ferrari Driver Academy in 2021 opened a path no female driver had previously taken within Ferrari's official young driver structure. Her subsequent progression through Italian F4, FRECA, and F1 Academy demonstrated consistent development, and her 2025 runner-up finish in F1 Academy — decided at the final race of the season — established her among the foremost female racing talents of her generation.