Weber was born in Mainz on 29 August 1994. He showed early promise as a thrower, but dropped athletics as a 12-year-old to concentrate on handball, the sport of his elder brother Patrick. He returned to the javelin four years later, immediately qualifying for the 2011 German youth championships; coached by Stephan Kallenberg, Weber developed rapidly as a thrower, but quit handball only after injuring himself in a game in 2012. At the 2013 European Junior Championships in Rieti Weber took gold with a fifth-round throw of 79.68 m, a personal best and the best in the world by a junior that year; he narrowly defeated Ukraine's Maksym Bohdan, who also threw beyond the previous world junior leading mark.