It's kind of confusing so bear with me. The Virginia governor was exceptionally weak, elected by the state legislature and being forced to work with an executive council also appointed by the legislature. This meant that rapid action was very difficult something that Jefferson had bemoaned as a wartime governor. Another example of the inefficiency was when Nat Turner revolted Governor Floyd was forced to wait until a member of the executive council returned so he could call out the militia

The convention of 1830 largely was a showdown between Western Virginians and Eastern Virginians. Westerners wanted a more democratic system (Virginia had very tough property voting laws) and a stronger governor who was elected by the people. Easterners wanted a weak governor beholden to the legislature, and the property requirements were set in such a way that the East would always control power in the State

It seems that initially the Governor's council was gotten rid of but the selection of the governor by the legislature remained now with term limits and a three year term, likely as a concession to Westerners. Ultimately it didn't matter as right before the convention ended a new vote was taken which put the executive council back into place.

Property requirements for the franchise were modestly eased but power remained with the east as did state economic investment. It wouldn't be until a few years before the Civil War that the governor's office was finally strengthened and westerners given equal access. By then though the damage was largely done and political animosity between east and west was entrenched

For More Information See

Democracy, Liberty, and Property:The State Constitutional Conventions of the 1820s

Virginia's American Revolution: From Dominion to Republic, 1776-1840