Re: More use = more value for money?
It was "forced" to put the service out to tender.
What I've not identified the exact circumstances that "forced" the service to be put out to tender in 2014. However, I suspect there was (Conservative) government interference, given the wording of the tender announcement:
"Provision of a service and system to enable the creation of high quality weather forecasts for UK (both national and regional) and global output."
[https://www.government-online.net/bbc-weather-services-weather-production-system/ ]
I suspect the Met Office would have to partner (with MeteoGroup?) to satisfy this requirement (doubt a Conservative government would permit a publicly funded agency to fully compete with (foreign) commercial entities as that just wouldn't be cricket.
Although this raises the question as to who was shortlisted, as suspect the tender was biased towards one company...
However, as MeteoGroup are a customer of the Met Office, the BBC are effectively still using Met Office data for their UK weather forecasts.