Cheesbrough smashed 36 runs including three sixes as his side took a 10 wicket victory over Baxenden.
Earlier professional Charles Dagnall did the damage as the visitors were dismissed for 35. Padiham stretched their lead at the top of the table with a comfortable victory over Cherry Tree.
They set a target of 190-3 with Pankaj Tripathi hitting 73 and Mark Harvey 83 not out. Gary Bolton scored a half century for Cherry Tree, but they were left holding out with nine wickets down.
Earby are in second place after beating Settle by eight wickets. Stephen Hipgrave took 5-26 as the Dalesmen were restricted to 89-8 and Applegarth professional Jonathan Harvey was 57 not out as his side took the points.
Barnoldswick beat Read in the last over. Ian Scothern scored 84 with the bat and his brother David captured six wickets as Read were dismissed for 146.
Jonathan Fielding enjoyed a superb afternoon scoring 86 for Clitheroe and followed up with eight wickets in their victory over Edenfield.
Oswaldtwistle took the points in their match with Whalley. Professional Zahir Hanif scored 75 and was backed up by Graham Parkinson 60. Skipper Gerard Metcalfe took 5-53 as Whalley were restricted to 112-8.
Ribblesdale Wanderers professional Shahid Nawaz scored 54 for Ribblesdale as they beat Blackburn Northern despite 64 from Paul Bromley.
Scores:
Barnoldswick 156-4 (7), Read 146; Cherry Tree 127-9, Padiham 190-3 (5); Clitheroe 147-9 (7), Edenfield 106; Great Harwood 37-0 (7), Baxenden 35; Oswaldtwistle 175-5 (5), Whalley 112-8; Ribblesdale Wdrs 133-5 (5), Blackburn Northern 132-9; Settle 89-8, Earby 92-2 (5).