Aero Weather advertises worldwide coverage and describes its procedures at its App Store entry but does not indicate if it has been approved by any Authority.
I have no doubt it I quite useful and might be far handier than government run outlets for the same information.
My understanding is that AeroWeather simply copies and displays the official METAR and TAF reports published by airfields.
How does that meet the FAR Part 135.213 wording of the regulation?
Whenever a person operating an aircraft under this part is required to use a weather report or forecast, that person shall use that of the U.S. National Weather Service, a source approved by the U.S. National Weather Service, or a source approved by the Administrator.
Is "Aeroweather" an approved source even if it does an accurate repeat of the approved weather source? Not nit picking....just pointing out something that can crop up in an Accident Investigation.
The UK CAA surely has similar but different wording and requirements....but I am sure it spells out what it considers "approved sources".
A casual drive by of the UK CAA website surfaced this......
Other Aviation Weather Sites
A paragraph or two before that entry was a comment about Electronic Tablets, etc.....and a caution for one to ensure the information obtained was the most current and accurate.
As to your suggestion that "in context" Aeroweather is an approved source needs more than an assumption to confirm or deny its being in fact an approved source does it not.
It shall certainly meet the OP's need as the approval that requires is that of the casual user.