"...I fail to understand the reference of (approximately...

"...I fail to understand the reference of (approximately 1,500psireduction in overbalance)
having something to do with a lower mud weight and solids content mud system.
Is it not the density of mud something different from the pressure or the mud system? "

1500psi overbalance means the pressure being exerted by the column of mud in the hole is 1500psi greater than the formation pressure.

The pressure exerted by a column of fluid is directly related to the density (weight) of the fluid.

Mud density is usually controlled via a weighting agent such as barite. While barite is part of the solids content of a mud there are also other solids in the mud which are produced by the drilling process.

Note that despite the 1500psi reduction in overbalance for the side track I still believe there was significant overbalance present.