When is a high pressure system associated with IFR/MVFR conditions?
In the temperate zone that covers the US and Canada, weather systems are generally related to frontal boundaries between warm/wet and cold/dry air masses, where the cold air pushes under the warm air and forces it up.

But in an area with a large weak high pressure system, you can get a lot of weather caused just by solar convection, depending on the humidity and lapse rate of the air in the mass.  The weather systems will be kind of randomly distributed around, instead of being arrayed along a frontal boundary.

You can see it in the chart you posted.  The weather along the Gulf coast is probably related to the stationary frontal boundary that is there, whereas the weather in the central states is from local convective conditions.

The absolute best practical book on aviation weather theory I've ever read is called the RCAF Weather Manual, written by the Royal Canadian Air Force as its primary weather training guide for pilots.  It is so clearly and logically presented I cannot recommend it enough.