Heavy trading in stocks of airlines likely to benefit from the bankruptcy of Braniff International Corp. dominated financial markets here today, although pressure late in the day caused an overall drop in what experts termed a tired stock market.

In particular, the stocks of carriers emphasizing Braniff's southern routes--American Airlines Inc. and Delta Airlines Inc.--were among the most active on the New York Stock Exchange today, as American jumped 1 5/8 to 16 1/4 and Delta rose 1 3/4 to 31 1/4.

Trans World Corp., meanwhile, was up 3/4 to 20 3/4, Eastern Air Lines Inc. jumped 3/8 to 6 1/2, and Northwest Airlines Inc. rose 1 to 29 1/8 as traders suggested that airline results soon would improve across the board with Braniff's fare-slashing less of a factor in competitive markets.

But the overall market performance was sluggish, with the Dow Jones industrial average falling 6.66 points to 859.11. Despite the airline stock surges, however, the Dow transportation index fell 0.48 point to 350.22.

Losers led gainers by 8 to 5 on the New York Stock Exchange, whose composite index slipped 0.49 point to 68.20.

Standard & Poor's index of 400 industrials fell 0.99 point to 131.75, and S&P's 500-stock composite index was off 0.95 point to 118.22.

Big Board volume was 58.23 million shares compared with 59.21 million Wednesday. Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 67.39 million shares.

The American Stock Exchange value index was off 0.77 point at 279.41.

The NASDAQ composite index for the over-the-counter market closed at 187.66, down 0.40 point.

"The most important factor in the stock market is that it's been going up for two months," said Larry Wachtel, a trader with Bache Halsey Stuart Shields Inc. "The market is tired and now seems to be the time to pull back a touch."

But market experts also noted that the Braniff collapse is a reminder of the increasing problems of corporate liquidity. "It could be that the bankruptcy will focus attention on how weak the economy really is," said Netwon Zinder, an analyst with The E. F. Hutton Group Inc.

Zinder also suggested that there appeared to be heavy selling late today because of President Reagan's press conference tonight and the continuing Washington budget stalemate.

At about 2 p.m., trading was suspended in Braniff stock and in four debt issues of the airline's subsidiary. Trading was halted until the announcement from Dallas concerning the Braniff bankruptcy petition.

As expected, Standard & Poor's cut its Braniff ratings to single-D on all Braniff issues.