how did what is now the Commonwealth of Virginia agree to give up a large portion of it's state like they did back then?
The commonwealth was busy trying to supply food, goods, and troops to fulfill what the CSA demanded of them.
Plus, there were valid fears of Union troops swarming and storming the walls and the gates of the bastions of leadership and finance within the commonwealth.
In my view, allowing a smallish portion of western Virginia to break away and join the Union was the most expedient strategy.
We also need take note of an historic event prior to the Civil War.
There was an effort by abolitionist John Brown, from October 16 to 18, 1859; to initiate/instigate a slave revolt across the Southern states by taking over the United States arsenal at Harper's Ferry, Virginia. It has been called the dress rehearsal for, or Tragic Prelude to, our Civil War.
The commonwealth leaders had bigger battles to fight than trying to stop the angry people of western Virginia from seceding.
By the way, the western region was admitted to the Union in 1863 as a new state, initially it wanted to be known as the State of Kanawha, but ultimately took the moniker of West Virginia.