Answer: This shrub blooms on wood produced the previous year, so do not prune it in the fall. Pruning it in summer, fall, winter or early spring would remove flowering wood and limit the blooms you would see. Any pruning of live wood to thin the plant should be done in the spring right after it blooms.
An exception to this would be removing any truly dead branches at any time they occur. Sometimes this plant suffers some winter dieback and this can be removed in the spring because dead wood will not flower anyway.
Generally a plant will have more foliage at the outer edges where there is more sunlight reaching the plant, so I am not sure whether the bareness you are seeing inside the plant is normal or not. Normally, the stems at the interior are alive and would have leaves at their tips.
This plant does best in full sun and average soil. New plants benefit from watering if needed to supplement rain so that the soil stays evenly moist the first growing season. In subsequent years they will still appreciate some deep watering in times of hot dry spells or drought. Water stress can cause the plant to die back somewhat as a protective measure.
Finally, excessively cold locations and/or exposure to cold drying winds can cause dieback during the winter. This plant is quite cold hardy, but microclimate could certainly make the difference between a good bloom performance and a poor one.
Other than that, it would be unusual to see extensive dead branches. You might want to consult with your county extension and/or professional nursery staff and see if they can help you trouble shoot. They might appreciate a photo of the shrub to help them in their diagnosis. Good luck with your weigelia.
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