The implementation of weather in MSFS has been problematic for more than a few of us. One issue that has been consistent so far is that the live weather setting seems to work okay for the first flight, but not after you complete a sector and go back out to the planner to load a new flight plan.
Last week, I stumbled across a workaround: Don't select live weather in the flight planner; select clear weather in the flight planner, then switch to live weather from the drop down menu after you've arrived in the virtual cockpit. It takes a few seconds for the new weather to appear, but it will, and more importantly, it will do so consistently, even after you've gone back to the flight planner.
The advantage to this is that the weather is dynamic, rather than static, as it is when you use a weather preset.
I haven't done a long term detailed comparison of the in-sim "live" weather to any real world METARs or TAFs, yet, but I did look at aviation weather forecasts for Alaska...VFR conditions with minimal icing, light to moderate turbulence, and winds from the ENE at 15-20 knots.
What I got for this morning's flight using live weather was visibility 10NM in rain with overcast at 3-4Kft, light turbulence, no icing, and winds from the ENE at 17 knots.
I'd call it "believable."