Weug was born to a Dutch father and a Belgian mother and grew up in Spain, competing under the flags of all three nations. She speaks English, Dutch, Spanish, Catalan, and Italian. She began karting at age seven and competed in multiple national championships including the Spanish Karting Championship, where she finished second in the Alevin Class in 2015.
From 2016, she competed on the international karting stage, most notably winning the WSK Final Cup in the 60 Mini category, defeating future Ferrari Driver Academy member Dino Beganovic. She made appearances in the CIK-FIA Karting European Championship and Karting World Championship across the following years.
In October 2020, Weug was selected as one of twenty female drivers between twelve and sixteen to participate in the FIA's Girls on Track - Rising Stars programme, with the prize being a place in the Ferrari Driver Academy. She progressed to the final selection alongside Doriane Pin, Julia Ayoub, and Antonella Bassani, and on 22 January 2021 was announced as the winner, becoming the first female driver ever to join the Ferrari Driver Academy.
Weug made her single-seater debut in 2021 in Italian Formula 4 for 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 reach the top ten in any main championship race, finishing 35th overall.
In 2022, she remained with Iron Dames and improved markedly, scoring points in multiple rounds including a sixth place on Sunday at Imola after starting third in mixed-weather qualifying. She added further top-ten finishes at Misano, Spa-Francorchamps, and Vallelunga, finishing fourteenth in the championship.
Weug stepped up to the Formula Regional European Championship in 2023 with KIC Motorsport. She achieved her best result in Race 2 at Spa-Francorchamps, taking a rookie class win and finishing sixth overall, and was the only KIC Motorsport driver to score points during the season. She accumulated 27 points across six top-ten finishes, finishing third among rookies and seventeenth among all 42 eligible drivers.
She returned to the FRECA in 2024 for the Mugello round with KIC Motorsport and made a further appearance in 2025 with Saintéloc Racing, replacing injured driver Tim Gerhards at the fourth round.
She was also selected alongside Iron Dames racer Doriane Pin and W Series drivers Nerea Martí and Irina Sidorkova for a one-day FIA Formula 3 test at Magny-Cours in November 2021.
Weug moved to F1 Academy for the 2024 season, racing with Prema Racing and representing Scuderia Ferrari. She secured one win — in Race 3 at Abu Dhabi — eight podiums, and one fastest lap, finishing the season third overall.
She retained Ferrari backing for 2025, switching teams to MP Motorsport. She won Race 2 at Jeddah, her home race at Zandvoort, and Race 2 at Singapore, amassing three wins and nine podiums. Weug and Doriane Pin were the main championship contenders going into the Las Vegas finale, the first time the title had been decided at the final event, where Weug finished second overall — her best result to date in F1 Academy.
For her runner-up finish in the 2025 F1 Academy championship, Weug was given the opportunity to test a Ferrari 296 GT3 with AF Corse in December 2025, fully funded by F1 Academy.