The 33-year-old striker, who will remain at Bramall Lane until the end of this season, made his debut for the Blades against Preston North End last Saturday.
Weir has stated that King's experience will be a vital asset to his side.
"Marlon has played at the top level and consistently for his country. He has tremendous attributes and we must do everything to maximise those," Weir told the club's official website.
"He is experienced and, first and foremost, an out and out goalscorer - he has a real know-how and can certainly help several of the players around him.
"Marlon wants to play games and score goals, but he has also shown a real willingness to contribute further and he will be a great asset to this football club."
King completed his move to the League One club last week.