Virginia National Bankshares Inc., which is trying to merge with First & Merchants Corp., posted record first-quarter profits, VNB officials said at the company's annual meeting yesterday in Norfolk.

Net income grew to $8.3 million ($1.10 a share), compared with $7.2 million (98 cents) a year earlier. Total assets on March 31 were $3.9 billion, up 23.6 percent from last year. Chairman C. A. Cutchins III attributed the performance to increased interest income, with a growing spread between the yield on earning assets and the rate paid for funds.

A definitive agreement between VNB and F&M will be given to the companies' shareholders this month, Cutchins said, and the owners will vote on the combination. He said he was optimistic that the merger could be completed this year.

Robertshaw Controls Co. rocketed back from the recession by posting first-quarter profits of $2.7 million (76 cents), compared with $385,000 (11 cents) in 1982.

Sales for the quarter were $86.9 million, compared with $85.1 million last year. Robertshaw, based in Richmond, makes thermostats and other control devices.

President and Chief Executive Ralph S. Thomas cited continued cost controls and a stronger economy--especially in the appliance, residential and automotive markets--for the huge jump in earnings.