Both Deutzia and Weigela should be pruned in the summer after flowering.
They both bear their flowers on short lateral growths produced from last year's wood.
' Without regular pruning to encourage development of vigorous, young growths from close to ground level, many of the shrubs in this group tend to become densely twiggy, often top-heavy, and the quantity and quality of flower deteriorates. The removal of spent flowerheads also prevents shrubs from expending energy in seed-production.'
'...as plants mature, more drastic pruning may be required to encourage groth. After the third year, up to one fifth of the oldest stems may be cut back annually to within 5-8cms of the ground.'
Renovation - 'old, tangled or overgrown shrubs may sometimes be renovated by extensive pruning. Shrubs that respond well usually produce young growth from the base.... some shrubs do not tolerate drastic pruning... if in any doubt, stagger a programme of heavy pruning over a period of 2-3 years. Renovate deciduous shrubs after flowering, or when dormant' e.g.
a) Drastic Renovation - Cut out all weak and crossing stems and shorten main stems to 30-45cms above ground level, ensuring that a balanced framework is left. Apply a slow-release fertiliser at 120gms/sq m and mulch around the shrub to a depth of 5-10cm. Keep the shrub well watered throughout the summer. During the following season, a mass of shoots should grow from beneath the cuts on the main stems. Retain only 2-4 of the strongest on each stem to provide the new branch framework' (cut the excess off during the dormant season on deciduous shrubs). In the following spring some secondary growth may occur where the shoots have been cut - rub these out.
b) Staggered Renovation - prune (after flowering) half of the oldest stems to 5-8cm of the ground, & where possible cut back the remaining stems by about half to a new vigorous replacement shoot. Apply slow release fertiliser, water & mulch. The following year, repeat the process on the remaining old stems.... OR do this over 3 years, i.e. cut back one-third of oldest stems almost to ground level, each year.
(RHS Gardening Book)