If Virginia and West Virginia never split, Trump's raw vote margin in West Virginia would have been enough to overcome the margin of defeat in Virginia, granting Trump the 13 electoral votes of Virginia
West Virginia would have handed Virginia to Mitt Romney in 2012 as well, if I am not mistaken. Ironically, Bill Clinton would have won the unified state in 1996, because of his strength in West Virginia (which he won 52-37% over Bob Dole that year). Dole won Virginia itself 47-45%. Jimmy Carter also would have won the unified Virginia in 1976.
You are right, it would tip Virginia to Romney. Interesting how there are four times when Virginia is tipped because of West, but I don't know of a single time west gets tipped because of regular virginia
1916 works. It's rare historically because VA had the Deep South version of strict poll tax prior to 1964 (prior to 1966 in state level elections), so there were shockingly few votes despite the larger population. From 1968-present, it has generally been decided by close margins, while WV basically went straight from Dem landslides to GOP landslides.
It's likely to happen in 2020 unless WV is like 75% Trump.