Hampshire 270 for 5 (Weatherley 78, Holland 74) lead Gloucestershire 229 (Phillips 47, de Grandhomme 4-31) by 41 runs
Having taken the final four Gloucestershire wickets for only 15 runs inside six overs of day two to bowl the hosts out for 229, Weatherley and Holland shared a partnership into the 52nd over of the reply.
Weatherley made 78 - his first half-century of the season - and Holland continued his fine campaign with 74 - the sixth score of 50 or more for Hampshire's leading run scorer.
When they were finally parted, Gloucestershire mounted a comeback taking five for 58 but they are playing catch-up in a game they now cannot afford to lose.
The home side resumed 214 for 6 with a second batting point in their sights but it proved a disastrous opening.
Jack Taylor, resuming on 34, fell to the 11th ball of the day as a sharp lifter from Kyle Abbott caught him on the glove and popped up for midwicket to run in and take a good catch.
Two balls later, the other overnight batsman, Ollie Price on 18, went to hook Colin de Grandhomme and gloved behind, Hampshire clearly having done their homework on the 20-year-old.
Matt Taylor propped forward and was lbw next ball and Gloucestershire had lost three wickets without adding a run. Dan Worrall pulled Mason Crane to midwicket and Gloucestershire were left with only one point.
With a spring in their step, Hampshire's openers gave their side a perfect start.
Weatherley drove Worrall through cover and Matt Taylor through mid-on before a thick-edge to third man raised fifty in 101 balls.
Holland had the home attack pulling their hair out with his tendency to play to leg. He flicked three boundaries through the on-side and punished a wide ball from Taylor in his 129-ball fifty.
Gloucestershire were seeing their dreams of Division One disappearing quickly but struck on the stroke of tea as Glenn Phillips found some turn and Holland's inside edge. Phillips then held Weatherley and Tom Alsop, for 15, at slip.
Tom Prest, on 18, and de Grandhomme, for a five-ball duck, both pushed at balls and were held by Ollie Price in the cordon - the first an outstanding one-handed take - but Nick Gubbins and Lewis McManus took Hampshire to the close in command.