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This could be due to high Nitrogen in the soil. This will cause lots of green leaves and no flowering.
You can add phosphorous to promote flowers. Bone Meal is a good way to do this.

Also proper pruning. Weigelas bloom on old wood.

Here are some links to help you.

https://www.gardeningknowhow.com/ornamental/shrubs/weigela/pruning-weigela.htm
https://www.gardeningknowhow.com/ornamental/shrubs/weigela/growing-weigela.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/bone-meal-fertilizer.htm

The best way is to prune them into a more compact shape. See this article for instructions:
https://www.gardeningknowhow.com/ornamental/shrubs/weigela/pruning-weigela.htm

Yes, this plant should do well in the climate of Atlanta.

This depends on your zone. In my zone 4 location weigelas are just leafing out now due to bad weather we've had they're a little delayed this year. Also are these plants you received potted or bareroot? If bare root pot & water them and wait & see. If potted, try snapping off some branches by bending them back toward themselves. If the branches just snap right off and are dry and brown inside, their probably dead. If the branches are flexible and do not break easily or break with fleshy green & white inside they're still alive.

Though LED lights that run all night have been known to interrupt a plants normal growth, it's doubtful your low wattage landscape light is the cause of your plants die back.

It is more likely attributed to winter die back.

Prune back the dead parts of the plant.

https://www.gardeningknowhow.com/ornamental/shrubs/weigela/growing-weigela.htm
https://www.gardeningknowhow.com/ornamental/shrubs/weigela/pruning-weigela.htm

This is a Weigela.

https://www.gardeningknowhow.com/ornamental/shrubs/weigela/growing-weigela.htm