So, long-time lurker here. Doesn't say this on the profile, but I'm a meteorologist.
I think these days it's strongly preferable to have an advanced degree for most parts of the field. If you're doing broadcasting, there seems to be a bias against advanced degrees (they're looking for a communicator, so an advanced science degree is an overqualifier for most stations). But generally, a master's degree makes you a stronger prospect for job openings, and will allow you to advance further.
It's a double-edged sword with PhDs, however. The education is a plus. But, many private companies recognize that PhDs expect to be paid that much more, and that doesn't fit with a lot of bottom lines. If you're doing a PhD, it might make it harder to find an opening, as you're overqualified for the entry-levels.
I opted to stop at master's level and followed some of the other recent masters' grads from my program into the energy industry. Most of my colleagues who did PhDs are in some combo of research/academia, and the ones who stuck with the bachelor's either did broadcasting or left the field. That's been my experience anyway.
P.S. On another note, for NWS, I believe 15% of their hires had advanced degrees in 1985. today, the number is more like 85%. Unless you're a SCEP or something, you'll likely need a master's to get a job offer from the NWS.