Follow up question. Was there any movement or plan to reunify the two states in the 20th century?

An excerpt from the inaugural address of the first governor of West Virginia, Arthur I Boreman, on June 20, 1863:

"West Virginia should long since have had a separate State existence. The East has always looked upon that portion of the State west of the mountains, as a sort of outside appendage - a territory in a state of pupilage. The unfairness and inequality of legislation is manifest on every page of the statute book; they had an unjust majority in the Legislature by the original Constitution of the State, and have clung to it with the utmost tenacity ever since; they have collected heavy taxes from us, and have spent large sums in the construction of railroads and canals in the East, but have withheld appropriations from the West; they have refused to make any of the modern improvements by which trade and travel could be carried on from the one section to the other, thus treating us as strangers; our people could not get to the Capital of their State by any of the usual modes of traveling, without going through the State of Maryland and the District of Columbia. The East and the West have always been two peoples. There has been little intercourse between them, either social or commercial. Our people seldom visit the East for pleasure. The farmers do not take their stock, grain, wool and other agricultural products there to sell; the merchants do not go there to sell or buy; the manufacturers have no market there; indeed, we have had nothing to do with the Eastern people, except that our Senators and Delegates have gone to Richmond to sit in the Legislature and our Sheriffs have gone there to pay in the revenue as an annual tribute from this section of the State for the inequality and unfairness with which we have always been treated by them. Our markets, our trade and our travel are North and West of Virginia, through natural channels, or those constructed through the enterprise of our own people, or such means as they could procure. The mountains intervene between us, the rivers rise in the mountains and run towards the Northwest; and, as if to make the separation more complete, Eastern Virginia adopted the fatal doctrine of secession, while the West spurned and rejected it as false and dangerous in the extreme. Thus nature, our commerce, travel, habits, associations, and interests, all - all say that West Virginia should be severed from the East. And now, to-day after many long and weary years of insult and injustice, culminating on the part of the East, in an attempt to destroy the Government, we have the proud satisfaction of proclaiming to those around us that we are a separate State in the Union." Source

So from the words of Governor Boreman it can be seen that there was a clear cultural divide between the western and eastern parts of Old Virginia. While the large, slave-dependent plantations of the Tidewater dominated the more eastern part of the state, the counties west of the mountains subsisted on small-scale farming and the salt mines focused around the Kanawha Valley (coal as an industry largely existed as an outgrowth of the saltworks before the Civil War). Along the Ohio River, industrial steel towns like Wheeling and Weirton were beginning to develop, cities that had more in common with Pittsburgh or Cleveland than they did with Richmond. There were distinct regional cultures that had developed between the two regions and there was no way that after the long fight for statehood (and after 30,000 some West Virginians had fought for the Union during the war) that West Virginians were going to submit to being controlled by Richmond again.

When Virginia held its secession convention in April of 1861, the delegates from what would become WV voted against secession 30-17 (HERE is a cool map from the University of Richmond showing the vote breakdown). After the vote passed, delegates from the western part of the state held a series of meetings throughout the summer in Wheeling. The eventual result of these meetings was the creation of the "Restored Government of Virginia" which governed the areas of the state under Union control and took Virginia's place in the US Congress. It was this Virginia government (whose legitimacy was debated) that gave authorization for the creation of the new state of West Virginia.

Following the war, the reconvened Virginia Assembly in Richmond passed legislation nullifying all the acts of the Restored Government, including the authorization for West Virginia's creation. Although the assembly likely did not realistically think that they could actually legislate WV out of existence (the dissolution of an existing state who had seated members in Congress is absolutely unprecedented in American history) what they did want was the return of Jefferson and Berkeley counties, located at the tip of West Virginia's eastern panhandle.

I won't delve into all the complicated legal arguments about why Virginia felt it had a case for the two counties (you can read a good summary from Wikipedia HERE), but suffice it to say that the Supreme Court ended up siding with West Virginia. My point with all this is to show that while there was no realistic chance of Virginia and West Virginia unifying again after the war, there was some legal wrangling over where exactly the border would lie.

In a final anecdote that is somewhat related, a second Supreme Court Case from 1911, also named Virginia vs. West Virginia, the Court forced West Virginia to be held responsible for 1/3rd of the state of Virginia's debt in 1861.

Nothing serious.

West Virginia and Virginia had little in common to begin with, and there had been tension from the beginning over culture (different sets of immigrants), politics, slavery (West Virginia was unprofitable for slavery), and economic. The Civil War just made the separation easy, as the western counties were far more pro-unionist.

Post-Reconstruction, the differences remained, and there has never been any serious attempt to reunify, especially since the culture has continued to drift apart.

/u/Das_Boot1 has given you a fairly lengthy answer, but I think he's doing a disservice by not mentioning Virginia v. West Virginia, the 1871 U.S. Supreme Court case that upheld West Virginia's succession from Virginia.

In summer 1861, the western counties of Virginia held a special election to send delegates to the Second Wheeling Convention, a secession meeting in Wheeling, the "arm" of West Virginia that divides Ohio and Pennsylvania. On Aug. 6, 1861, the delegates adopted a resolution calling for the secession of 39 counties and several more if their voters approved. Those elections took place on Oct. 24 that year, and the 39 counties (plus two others) voted to secede. In the following months, other counties were added to the new state, even though their voters had not approved seceding from Virginia.

Berkeley, Frederick, and Jefferson Counties were all under the military occupation of the Confederacy when West Virginians voted on their new state constitution. After liberation, Berkeley and Jefferson voted to join West Virginia. Frederick elected to stay with Virginia.

The state of Virginia opposed these votes. On Dec. 5, 1865, the Virginia Assembly approved legislation that supposedly repealed the secession of the West Virginia counties. This turned into a hot-button political issue. Congress weighed in during 1866, passing a resolution confirming the transfer of Berkeley and Jefferson counties. Virginia then sued, saying the 1863 elections that brought Berkeley and Jefferson into West Virginia were fraudulent.

In a 6-3 decision, the Supreme Court found the transfer was acceptable. While it did not (and really never did, as far as I can tell) officially recognize the creation of West Virginia as legal, its decision was a de facto acceptance of the issue. And 22 years later, in Virginia v. Tennessee, the court ruled that if two states ratify a boundary agreement, one state cannot later say that the boundary was set in error.

In 1911, 50 years after the secession of West Virginia, there was another Supreme Court case dealing with the secession. This time, it was a unanimous ruling that held that West Virginia was obligated by its constitution to pay one-third of Virginia's state debt as of Jan. 1, 1861. When the WV constitution was drafted, there was a provision that the new state had to assume "an equitable portion" of the debt Virginia had taken building roads, canals and other infrastructure in the boundaries of the new state.