Monthly bills for D.C. residents who heat their homes with gas will rise by an average of $6.34 to $76.62 under a rate increase approved yesterday by the D.C. Public Service Commission.

Bills for Washington Gas Light Co. customers not heating with gas will rise by $1.49 to a total of $18.77 a month, according to the PSC's figures.

PSC officials said the increases for the utility's 150,000 customers in the District are expected to yield the company an additional $11.9 million a year. Virginia customers are not affected.

A utility spokeswoman said the increases, which are expected to take effect in a week or 10 days, were disappointing and less than the company had requested. She said the company had asked for a total increase of $17.4 million.

The increase is the company's first in the District since March 16, 1979.

The monthly bills for the company's 90,000 residential heating customers and 43,000 residential nonheating customers were computed by the PSC under the assumption of use of 155 therms a month by heating customers and 115 therms by others.

In other action, the PSC ordered the company to begin reading meters on a monthly basis instead of every other month. The new procedure is to take effect 60 days after the new rates begin.

The commission also ordered the utility to increase to 8 percent the interest paid on customer deposits. Some customers now earn 5 percent while others earn 6.