Center Controller reported an aircraft entered severe turbulence and lost 3;000 feet before stabilizing.

Narrative

At the time of the event I was training a developmental at R49. Weather impacted the sector and aircraft were deviating from their route. Ride conditions were only light chop and most aircraft were not requesting a different altitude for chop. Deviations and volume made the sector complex. My trainee issued the weather to Aircraft X on initial check in and was cleared to deviate to the right for the area of precipitation. Aircraft X deviated for the weather and several minutes later called back on course to PRMUS intersection. There was an additional precipitation cell at his 11:00 and approximately 30 miles; I am unsure if my trainee issued the precipitation to Aircraft X. Aircraft X reported extreme turbulence and lost 3;000 feet. I instructed Aircraft X that he was cleared to level off at any altitude that he could maintain and he did.Volume and weather deviations made the sector complex. If less volume was in the sector we would have had more time to make sure everyone was clear from weather.