The preppy version of the Hatfields and the McCoys, featuring the feuding Greenwich families of the Weickers and the Bushes, reached another shoot-out stage tonight at the opening of the Connecticut Republican Convention here.

Sen. Lowell P. Weicker Jr., an independent-minded maverick, arrived in the unusual role of the "establishment favorite" to receive the party endorsement for a third term against the challenge of Prescott Bush Jr., older brother of Vice President Bush.

Prescott Bush conceded in an interview this morning that Weicker would out-poll him Saturday among the 933 delegates. But he insisted that he would have "a lot more" than the 20 percent of the votes he needs to force Weicker into a Sept. 7 primary, where, Bush said, "I will beat him for sure."

Weicker, for his part, said that Bush's campaign has "gone steadily downhill. To know him is not to like him."

Weicker's campaign manager, Tom D'Amore, said Weicker had "a long-shot chance" to hold Bush below the 20 percent figure that would give him a second chance under Connecticut's "challenge primary" law.

The origins of the antagonism between Weicker and the Bush brothers--fellow-millionaires, fellow-Yalies and fellow-residents of the swanky Fairfield County suburb of Greenwich--are cloaked in mystery. But the feud became public when Weicker refused in 1974 to vote to confirm George Bush as director of the CIA.

During the 1980 presidential primaries, after Weicker had abandoned his own abortive campaign for the nomination, he infuriated the Bush clan by making the public charge that George Bush, while Republican national chairman in the Watergate period, had asked Weicker if he should destroy records of possibly illegal contributions to a secret Republican 1970 campaign fund.

George Bush said that statement was "an absolute lie." In October, 1980, when Weicker gave President Reagan a lukewarm endorsement, he specified that it did not apply to his running-mate, Bush.

Bush is not the only fellow-Republican to feel Weicker's scorn. He was a biting critic of Richard Nixon's entourage as a member of the Senate Watergate Committee, and in 1980, declined to endorse conservative James L. Buckley, the GOP nominee for the Senate against Sen. Christopher J. Dodd (D-Conn.).

But Weicker has never lost an election in nine tries, and his demonstrated appeal to independents and some Democrats has made him the only Republican able to retain statewide office in the last decade.

Despite that record, there was such antagonism toward Weicker among the state's 440,000 enrolled Republicans that Prescott Bush was far ahead of Weicker in a primary-election poll when he entered the race last January. He charged that Weicker too often "thumbs his nose at his party, his president and the best interests of his state." There was widespread speculation then that Bush would be strong enough to force Weicker to seek reelection as an independent.

But the 59-year-old insurance executive, who had been active as a fund-raiser for the GOP but had never been a candidate beyond the local level, proved to be less than adept as a platform performer.

He told an audience in March that, when it came to illegal immigrants, "I'm sure there are people in Greenwich who are glad they're here, because they wouldn't have someone to help in the house without them."

Another time, he issued a policy paper on crime advocating "determinate sentences," then told a reporter that he had never heard that phrase used before and didn't know what it meant.

While Bush was stumbling, a series of public and private polls showed Weicker significantly stronger than Bush in a match up with Rep. Toby Moffett, the Democratic senatorial nominee. The polls show Weicker-Moffett about even, while Bush trails Moffett by 12 points or more.

In part because of those polls, a series of top GOP state officials, including party chairman Ralph Capecelatro, switched from neutral or pro-Bush positions to endorse Weicker in the past two weeks, finding pragmatic reasons to ignore Weicker's past blasts at their political skills and principles.

This morning, Weicker--the old insurgent--presided benignly at state GOP headquarters as Capecelatro and two aspirants for the gubernatorial endorsement announced a "unity slate" of convention officers. Bush--the establishment man--was not even invited.

"If you'd said a few weeks ago you would find this assemblage in this office," Capecelatro remarked, "somebody would have asked what you are smoking."

Bush, a self-proclaimed moderate, finds himself in the odd position of having his strongest support from right-wing elements, including the Connecticut offshoot of the National Conservative Political Action Committee, headed by Peg Dolan, the mother of NCPAC Chairman Terry Dolan. The group is running anti-Weicker television ads.

But Bush also has cheerleaders in Washington. Lyn Nofziger, former press secretary and political aide to Reagan, said this spring that Bush had "the silent support" of everyone in the White House.

Frederick K. Biebel, deputy chairman of the Republican National Committee and a former state GOP chairman, gave Bush an endorsement to offset Capecelatro's surprise move to Weicker last weekend.

But Weicker has enlisted Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) and a number of conservative senators--including his tennis partner, Paul Laxalt (R-Nev.)--for public endorsements. A Baker aide said yesterday they would try to get the White House to "call off" Bush from forcing a primary if Weicker wins the expected endorsement Saturday.

The Bush camp immediately got a hands-off statement from Edward Rollins, the White House political director, and Prescott Bush said this morning, "I would not drop out, even if they asked me."

George Bush is publicly uninvolved in his brother's race, but the delegates were invited to a reception tonight honoring "Prescott and George Bush," the latter being the son of the vice president and a Midland, Tex., oil man.

The mother, two brothers and sister of the vice president were also present, in case anyone was in doubt where family loyalties lie in the latest round of Greenwich's famous feud.