Weather regularly grounds airlines - the problem is not weather in flight, the problem is weather at specific airports, and with how southwest flight graph is constructed the knock on effects can be huge (it's also why in hub-spoke setups you have huge investments into making hubs capable of dealing with extreme weather)
Which still doesn't explain why other airlines operating at these ports didn't experience this kind of large scale disruptions and why no weather maps were shown (as far as I know) to back up these claims.
Other airlines were disrupted, but not to the same level, due to different level of dependance on said stop. The second most affected airline IIRC had Jacksonville as minor stop, and out of all impacted, only Southwest used what they call "line flow" flight planning. Which results in Southwest being the only one to end up with stuck planes that were supposed to service a many routes way further away.
Most low-cost airlines operate on a sort of "distributed hub-and-spoke" (many small hubs instead of one/few big ones), with plane going bidirectionally on a route to non-hub airport before any route switching happens. This means that so long as the "hub" isn't severely impacted your disruption is somewhat contained and you still have access to a fleet of planes&crews that can be reassigned.
A pattern like this:
H->A->H->B->H->C->H ;; H = "Hub"; A,B,C - spoke airports
Disruption at A,B, or C doesn't block unrelated flights, only disruption at H.
Southwest instead flies like this
A->B->C->D->E->F->G
If B is in any way blocked, flights B->C, C->D, D->E, E->F, and F->G are all going to be disrupted, possibly without replacements plane/crew combinations available. If the disrupted airport has a lot of overlapping "lines" like that, the disruption quickly turns catastrophical.
Also, appears that at least some approaches were manually vectored recently at KJAX, which isn't fun if there's a shortage of controllers.
Because it was not just weather. It was combination of weather with low staffing of local ATC and disruptions to flight patterns. Weather is just one of the triggers.
