[2] Weber graduated from Alvin Community College and in 1977 earned a BS in public affairs from the University of Houston–Clear Lake.

[4] After State Representative Glenda Dawson died on September 12, 2006,[5] a special election was held on December 19.

[17] Weber also cosponsored a resolution disagreeing with the Supreme Court decision in Obergefell v. Hodges, which held that same-sex marriage bans violated the constitution.

[18] In April 2015, Weber met with Aleksandr Torshin, the alleged handler for Russian spy Maria Butina,[19] according to internal documents from Center for the National Interest.

In December 2020, Weber was one of 126 Republican members of the House of Representatives to sign an amicus brief in support of Texas v. Pennsylvania, a lawsuit filed at the United States Supreme Court contesting the results of the 2020 presidential election, in which Joe Biden defeated[21] incumbent Donald Trump.

The Supreme Court declined to hear the case on the basis that Texas lacked standing under Article III of the Constitution to challenge the results of an election held by another state.

[22][23][24] House Speaker Nancy Pelosi issued a statement that called signing the amicus brief an act of "election subversion."

In September 2021, Weber submitted a resolution to impeach Biden "for perpetuating a perception that Afghan security forces were winning the war against the Taliban.

[28] In August 2021, Weber co-sponsored a resolution to impeach Alejandro Mayorkas, Biden's Secretary of Homeland Security.

[30] In February 2023, Weber, along with Representatives Lizzie Fletcher (D‑TX 07th), Nancy Mace (R‑SC 01st), Abigail Spanberger (D‑VA 07th), Don Davis (D‑NC 01st), and Anna Eshoo (D‑CA 16th), introduced the Reinvesting in Shoreline Economies and Ecosystems Act, which aims to share federal offshore wind power revenue with states for coastal protection and restoration work.