Weber, who's coming off a two-year deal that averaged $950,000 per season, will make $1.5 million in each of the next two years and $2 million in 2015-16, according to the Buffalo News.
The 25-year-old has spent parts of five seasons in Buffalo. He played 42 games in 2012-13, recording one goal, seven points and a plus-3 rating with 70 penalty minutes. He led the Sabres with 92 blocked shots and ranked second on the team with 122 hits.
The Pittsburgh native has appeared in 174 games for the Sabres, scoring six goals and 32 points along with 236 penalty minutes, with a plus-6 rating.