Marriott Corp. will continue to expand aggressively this year, but may have trouble maintaining growth in its profits, President J.W. Marriott Jr. told stockholders at the company's annual meeting yesterday.

"We believe Marriott will have a good year overall in 1982 but, because of the economy, it will not be an easy year," the chief executive said. "We're going to have to put extra effort forth to come close to our profit objectives."

With the recently completed acquisitions of Gino's and Host International and internal expansion, Marriott's sales should grow by $600 million this year to $2.6 billion, he predicted.

While the recession has hurt the hotel and food business, Marriott's lodging division posted a slight improvement in the first quarter, the Marriott president said. Answering a shareholder's question, he said the gain was "less than one percent, but most of our competitors showed occupancy declines" ranging from 0.5 percent to 4 or 5 percent.

Marriott opened 23 new hotels last year, expanding its system to 100 units with more than 40,000 rooms. This year, 16 more hotels are coming and, by the end of 1985, "We plan to have over 150 hotels with about 75,000 rooms," he said. "Financing for most of the properties coming onstream through 1984 has already been arranged."

With the help of heavy promotion, Marriott's restaurants had a good first quarter, thanks to stable food prices and improved productivity. A change in menus has helped the Big Boy chain, Marriott added, and the restaurant business is "beginning to improve with better weather and a better economic outlook."