Weightman made his debut for Nottinghamshire in a List A match against Hampshire in the 1980 John Player League. He made seven further List A appearances, the last of which came against Derbyshire in the 1981 NatWest Trophy. In his eight List A appearances, he scored just 44 runs at an average of 5.50, with a high score of 17. He made his first-class debut for the county against Lancashire in the 1981 County Championship. He made two further first-class appearances in 1981, against Leicestershire and Surrey, while in 1982 he made a single appearance against Cambridge University. In his four first-class matches, he scored a total of 175 runs at an average of 29.16, with a high score of 105. This score was the only time he passed fifty and came against Leicestershire.

Neil Ivan Weightman (born 5 October 1960) is a former English cricketer. Weightman was a left-handed batsman who bowled right-arm off break. He was born at Normanton-on-Trent, Nottinghamshire.