The 25-year-old Morpeth Harrier, from Lesbury, near Alnwick, crossed the line in 4:14.95. She had been at the front of the field in the early exchanges of what was a slow, tactical race in the Olympic Stadium, in Rio, Brazil. Fellow Team GB star Laura Muir came seventh in 4:12.88.
The race, which started at 10.30pm local time (2.30am GMT), was won by Kenya's Faith Chepngetich Kipyegon in 4:08.92. Genzebe Dibaba, from Ethiopia, took the silver in 4:10.27, while the USA's Jennifer Simpson secured bronze in 4:10.53.
Laura made the final by finishing fifth in her semi-final on Sunday night (local time), having scraped through her heats as one of the fastest losers two days before.
The Rio Games were Weightman’s second taste of the Olympics, after she finished 11th in the 1500m final at London 2012.