Somerset need to win to claim the title for the first time and were 144 for nine before Leach came to the wicket and made 11 from 36 balls as Roelof Van Der Merwe hit 60 to take their side to a total of 203.
In response, Essex had reached 25 without loss before the rain returned to signal a premature end to the day.
Only two overs were bowled at the Oval for Surrey's match against Nottinghamshire, with the home side adding two runs to their overnight total, to take the score to 248 for two. Ollie Pope remains unbeaten on 79, with Scott Borthwick on 109.
No play was possible at Edgbaston for Warwickshire's clash with Yorkshire or at Canterbury for Kent's match against Hampshire.
In Division Two, Glamorgan's slim hopes of promotion were dealt a blow by the weather and BJ Watling in their match against Durham at the Emirates Riverside.
Only 15 overs were possible due to the weather, as Watling recorded his 17th first-class century, to finish the day unbeaten on 104 as Durham reached 262 for eight.
Luis Reece claimed a 50th Championship wicket of the season for Derbyshire as Middlesex reached 199 for five at Lord's.
Only 52 balls were possible, as Dawid Malan reached 66 not out, with Reece taking the wicket of Martin Andersson to reach his milestone. Malan's overnight score left him just one run shy of 1000 championship runs this summer.
A strong eighth-wicket partnership of 96 between David Wiese and George Garton put Sussex on top in their clash with Worcestershire at Hove.
The first half of the day was washed out, but Wiese and Garton made up for it. Wiese struck a powerful 47 from 72 deliveries while Garton hit a career-best unbeaten 59 as Sussex reached 299 for eight.
There was no play at Bristol for Gloucestershire's game against Northamptonshire, or Leicestershire's clash with Division Two champions Lancashire.