States like Virginia are not weighted any more heavily. The formula for base delegate allocation is based on two numbers: proportion of Democratic votes in the last three elections, and proportion of electoral votes. For the former, you add up the number of votes in that state for the Democratic ticket in 2004, 2008, and 2012; add up the number of votes nationwide for the ticket in those three years; and divide the first number by the second number. For the latter, you just divide the number of electoral votes by 538. The two factors are equally weighted: a state's base delegate allocation is 3,200 times the average of the two factors. After the base is computed, adjustments are made based on scheduling of the primary (you get a bonus for a later primary, and if your primary is later and is on the same day as the contests in at least two neighboring states you get an even bigger bonus), and a bonus of 15% of the base is added for pledged party leader and elected official delegates (not superdelegates, those are totally separate).
Within each state, 25% of the base delegates must be awarded at large, based on statewide results. The remaining 75% of the base delegates must be awarded at the congressional district level or smaller. For allocation of district delegates between districts, there are four acceptable ways to determine it. You can give equal weight to population and to total Democratic votes in the last two presidential elections; or equal weight to Democratic votes in the last presidential and last gubernatorial election; or equal weight to total Democratic votes in the last two presidential elections and number of registered Democrats as of January 1, 2016; or equal weight to those three formulas.
With this approach, states with more support for the Democratic candidate in the past few cycles get more delegates than equal-sized states with less support. However, a bigger state with fewer Democrats might get more delegates than a smaller state with more Democrats. At the district level, you can do that, but can also choose to ignore population and exclusively consider the number of Democrats (or people who supported Democrats).
No bonus is given for being a swing state.