May Department Stores Co., the nation's second-largest department store retailer and owner of the Hecht Co. in Washington and Baltimore, yesterday raised its dividend rate and reported record sales and earnings for 1976 despite a dip in fourth-quarter profits and sluggish growth for the full year.

Profits of the May Co. totaled $69.4 million ($3.06 a share) in the year eneded Jan. 29 compared with $66.7 million ($2.94) the previous year. Sales rose by 8.5 per cent to $2.1 billion.

In the fourth quarter alone, however, the St. Louis-based company's profits fell to $40.5 million ($1.79) from $41 million ($1.82) a year earlier. Sales rose from $664.6 million to $720.6 million.

Chairman David E. Babcock and president David C. Farrell characterized 1976 as "another year of continued growth," despite an "abrupt and unexpected" decline in purchashing that began last pring and lasted until Christmas.

"We moved quickly to liquidate our excess stocks, resulting in heavy markdowns in the second and third quarters," the May Co. officers said.

Braced with management's forecast for "a resurgence in apparel in 1977," directorso fot he company voted to increase the payout on common stock from 28 to 29 cents a quarter effective with a June 15 distribution.