Hampshire 79 and 92 for 3 (Overton 3-24) trail Somerset 336 (Overton 74, Abell 64) by 165 runs
A Craig Overton-inspired Somerset assumed full control against Hampshire as the visitors dominated the second day at the Ageas Bowl.
Overton - the leading wicket-taker in the LV=County Championship - demonstrated his batting credentials by top-scoring with 74, then starred with the ball as his side opened up a 165-run lead, Hampshire closing on 92 for 3 in their second innings.
Overton struck 10 fours on the way to his 13th first-class fifty, before he removed opener Ian Holland, Tom Alsop and nightwatchman Kyle Abbott during a hostile spell of bowling late in the final session.
Alsop and Weatherley had dug in admirably in a 56-run stand before Alsop fell for 32 five overs from the close when he lobbed an easy catch to Josh Davey.
Overton struck again in the penultimate over of the evening when he trapped Abbot lbw for a duck for his 30th wicket of the campaign.
Weatherley was unbeaten on 31 alongside new batter Sam Northeast, with the pair to resume their innings at some stage on Saturday with heavy rain forecast in Southampton.
Somerset started the day on 142 for 5 and added another 47 before skipper Tom Abell's stubborn innings was ended on 62 by a ball that nipped back into the top of his off-stump from Abbott.
Nightwatchman Jack Leach, dropped when on three in the final over of the first day, made the hosts pay for that mistake with an entertaining 34. But the England spinner perished after trying to lift Keith Barker over the slips cordon only to find the hands of Liam Dawson.
Somerset's deep batting line-up then proved its worth as 143 runs were put on for the last three wickets, spearheaded by Overton. He was ably supported by Steve Davies and Lewis Gregory, who each scored 33, as Somerset, who sit in second spot in Group Two, one place above Hampshire, built up a handsome 257-run lead after recovering from 36 for 3 to be 336 all out.
Left-arm veteran Barker was the pick of the home bowlers finishing with 4 for 67 alongside South African quick Abbott who took three wickets.