Timescale has a direct effect on the game's volatility setting, which governs the likelyhood of a weather to change to another weather. Weather changes on a cycle. For each cycle, an internal roll is made to determine if the weather should change or keep its current state. If a weather profile has a high volatile setting, there's a higher chance for a weather to change to a different weather on the next cycle.
In theory, volatility should be directly tied to timescale, so a halved timescale would halve volatility as well. This does not appear to happen correctly, and instead you will get a single weather type for days. That is why most weather mods advise against changing timescale, because it screws with the intended weather cycle.
It's not as much about timescale being a complete no-no for weather (I use sub 10 myself in any game), but more about having to not use timescale values much lower than 8-10. You can easily experiment to find out where your timescale sweetspot is.
If you find that weather still changes too slow, you can increase Volatilty, or even edit weather chances in FO4Edit easily. Lookup "DefaultClimate" with FormID 15F under "Climate", copy DefaultClimate as override into a new file, scroll all the way down in the right field and increase Volatility setting.
