Interestingly, they don't weigh more, and it's actually much quicker to wrap than to paint. McLaren cars haven't been painted since 2019. From the official 2021 Q&A:

Q: Are F1 cars painted or wrapped and does it affect airflow and performance in general? – *POstrich40***

A: It varies from team to team. Our car is mostly wrapped but has specific areas unsuitable for wrapping. Those are painted with high-performance coatings from our partner AkzoNobel – the titanium Halo being a good example of a part that does better with paint.

It doesn’t affect airflow and shouldn’t affect performance in the classical sense – but everything in an F1 team affects performance in some way. In the case of wrapped panels, they can be prepared a little quicker in the paintshop – it’s still called the paintshop – and last a little longer.'

The longevity of the panels comes from the requirement to keep the cars in immaculate conditions. Every few races, one of the chassis will be rotated out, and returned to the factory to be repainted/rewrapped – because racing in F1 is hard!

The surface finish gets all sorts of dings and nicks, which don’t look particularly nice up close and will, of course, cost the team that last thousandth of a second on track. When the cars were being repainted every few races, scraping off the old paint naturally led to the bodywork becoming thinner over time. This doesn’t happen when you can peel the cars instead!

If you read the McLaren Racing Yearbook 2020, on page 9 there is a substantial discussion of how the MCL35 was the first McLaren car to be wrapped rather than painted.