Weaver worked for Republican congressmen Phil Gramm and Tom Loeffler, as well as Bill Clements. Weaver was executive director of the Republican Party of Texas ; was a Texas leader in George H. W. Bush's campaigns for president in 1988 and 1992; and worked for Gramm in his unsuccessful 1996 bid for the presidency.
McCain adviser
For a decade, Weaver was a senior adviser to Senator John McCain of Arizona. He was described as one of McCain's "closest advisers" and "an architect of McCain's 'Straight Talk Express,'" and left the McCain campaign in July 2007, along with campaign manager Terry Nelson, political director Rob Jesmer, and deputy campaign manager Reed Galen, following several consecutive months of poor fund-raising. In 2004, Weaver appeared in the documentary film , which alleges that Karl Rove, former campaign manager and Deputy White House Chief of Staff to President George W. Bush, was behind a South Carolinapush poll during the 2000 Republican primary that used racist innuendo to undermine support for McCain by asking voters: "Would you be more likely or less likely to vote for John McCain for president if you knew he had fathered an illegitimate black child?" In 2008, Weaver made headlines within the Washington beltway during the John McCain lobbyist controversy when some American media personalities speculated about his involvement in an article published by The New York Times that questioned the propriety of McCain's relationship with lobbyistVicki Iseman. Weaver denied speaking to the paper without the campaign's approval. Weaver and Mark Salter are viewed as two of the aides who were closest to McCain.
Huntsman and Kasich aide
Weaver served as the chief strategist for Jon Huntsman's 2012 presidential campaign. After Mitt Romney's defeat in the November 2012 general election, Weaver tweeted, "In our party, intolerance can no longer be tolerated". By June 2015, Weaver had been hired to work on the prospective presidential campaign of Ohio Governor John Kasich. Acting as Kasich's strategist viewing the February 20, 2016 South Carolina primary, Weaver is quoted in The Atlantic as saying, "We want to do well enough to keep Jeb from doing well. If we knock him out of the race, it's a victory."
Post-2016
In 2019, Weaver and fellow Republican operatives George Conway, Steve Schmidt, and Rick Wilson wrote an op-ed published in the New York Times, calling for Donald Trump to be defeated in the 2020 presidential election. The four wrote, "The president and his enablers have replaced conservatism with an empty faith led by a bogus prophet." He serves as an advisor to The Lincoln Project, a super PAC organized by current and former Republican operatives opposed to the re-election of Donald Trump in 2020." In April 2019, Weaver signed a six-month contract with a subsidiary of Rosatom, worth $350,000 plus expenses, to lobby on “sanctions or other restrictions in the area of atomic energy, trade or cooperation involving in any way the Russian Federation” and submitted FARA registration form. However, after the report of the contract has been published, Weaver cancelled the contract.