Reynolds Metals Co., the nation's second-largest aluminum producer, yesterday reported a decline in fourth-quarter profits but higher earnings for the full year.

United Virginia Bankshares Inc., meanwhile, reported a 19 percent increase in fourth-quarter profits as well as a 15 percent gain for the year. But Bank of Virginia Co. said profits fell both in the recent quarter and full year while First American Bank of Washington posted a 21 percent gain for the recent quarter and a modest, 5 percent increase during all of 1980.

Richmond-based Reynolds earned $33.5 million ($1.71 a share) in the fourth quarter compared with $44.4 million ($2.31) a year earlier as sales rose to $906 million from $827 million. For the full year, Reynolds earnings were up to $180 million ($9.32) from $177 million ($9.25) as sales rose to $3.7 billion from $3.3 billion.

In the final period Reynolds wrote off $8.6 million (45 cents), the costs of closing several facilities.

Chairman David Reynolds described the year as "very good" despite the national recession. His company's aluminum shipments declined slightly to 1.32 million tons compared with 1.33 million tons in 1979. Because of near-term economic fluctuations throughout the world, "our performance this year will probably not match 1980 levels," Reynolds added. But he added that Reynolds is well positioned to take advantage of industry growth "if the economy in general improves."

United Virginia Bankshares, a Richmond holding company that is the state's largest banking business, said operating profits in the fourth quarter (not counting gains or losses from selling securities) was $9.5 million ($1.76 a share) compared with $8 million ($1.48 a share) a year earlier. For the full year, operating profits rose to $34.2 million ($6.35) from $29.6 million ($5.50).

Chairman Joseph Jennings, who attributed the higher earnings to increased interest income on loans, said UVB's earnings were equal to 17.3 percent on stockholders' equity (investment) in the holding company. Assets rose 7 percent to $3.45 billion while loan volume increased 13 percent to $2.22 billion. Statewide deposits rose 7 percent to $2.67 billion.

Bank of Virginia Co., another Richmond-based bank holding company with statewide operations, said fourth-quarter operating profits declined to $2.7 million (47 cents a share) from $3.6 million (72 cents) a year earlier. For the year, operating earnings fell to $13.2 million ($2.40) from $14.95 million ($3.15).

The company said that high interest rates and slackening loan volume combined to make the recent quarter the weakest period of the year.