Heritage Financial Corp., a Richmond savings and loan holding company, announced an agreement in principle yesterday to acquire United Savings and Loan Association of Arlington for about $7 million worth of stock.

The Richmond company said it will exchange 1.5 shares of Heritage common stock for each of the 350,100 United shares currently outstanding. Heritage has been trading in the over-the-counter market at $13.25 a share, making the offer worth about $20 for each United share.

A combination of the two companies would create one of the largest thrift institutions in Virginia, with combined assets of $280 million. Federal and state regulatory agencies as well as United stockholders must approve the proposal.

According to C. Linwood Clements, president of Heritage, his firm's Heritage SL has nine offices in the Richmond area and one office in Winchester, with assets of $2.12 million.

United, headed by chairman Charles M. Neviaser, has assets of $68 million and four branch offices in been quoted in the OTC market this Northern Virginia. United stock has been quoted in the OTC market this week at $8 a share, far below the Heritage offering price.

If the acquisition is approved, the Richmond SL& company will nearly equal in size the largest current S&L firm in Northern Virginia - First Financial of Virginia Co., of McLean. First Financial has $300 million of assets and is the owner of Washington Lee Savings and Loan, with two dozen offices from Northern Virginia to Fredericksburg.

United S&L opened for business in 1965 as a Virginia-chartered stock corporation, with deposits insured by the Federal Savings & Loan Insurance Corp. and initial capitalization of $1.5 million. It was formed by former builder and developer Arthur Pomponio.

In a 1976 proxy battle, however, the Pomponio group was ousted from management by an insurgent group that Neviaser headed. Eight directors voted to oust Pomponio in May 1976 and in a subsequent, close election, that action was upheld. Neviaser, a former president of the Fairfax County Chamber of Commerce, Previously had headed George Mason S&L, merged into United in 1967.

A spokesman for Pomponio said at the time that he had been ousted because he was named in litigation involving American Realty Trust, an Arlington real estate investment trust.

United has been growing rapidly under the management of Neviaser and president Robert Rush. Assets rose 30 percent in 1977 when the S&L earned $427,397 ;$1.22 a share). Directors of United have approved the Heritage offer, the officers said yesterday.

Earlier this year, Financial Mortgage & Realty Corp. of Washington acquired a 20.5 percent interest in United.