A Center Controller reported a departing aircraft temporarily lost control while encountering turbulence and weather. ATC had routed the aircraft through an area of known weather and turbulence

Narrative

I was working sector X when approach called and said we would be one route out the East gate until the weather closed the gate. About eight more air carriers came out on headings and I was told by the supervisor that the East gate was closed. Another four or five air carries came out of the East gate and the weather was rapidly closing and forming a horseshoe shape that can be very dangerous for aircraft. The last jet reported moderate turbulence through the hole. Aircraft X was departed and climbing out the East gate into a very dangerous thunderstorm; when they checked on I advised them of the weather and told them deviations are approved and if they need to turn around and return to ZZZ that could be worked out as well. Withing a couple of minutes Aircraft X said they needed to return to ZZZ and they were 'having issues with the plane'. They were getting moderate to severe turbulence and could not control the plane. I cleared them back to ZZZ via whichever turn was safest and gave them a descent to 16000 ft.; and shipped them to approach. The aircraft bounced around the weather and eventually ended up on the east side of the weather back in my airspace descending rapidly and was able to level off at 9000 ft. and continue on to ZZZ1. In the beginning of every summer we receive a weather briefing that states we should try to avoid weather by 20 miles if possible. Then all of that goes out the window when ZZZ2 has planes that 'need to get out' of the East gate. We are sacrificing safety to try and squeeze aircraft out of the gate and are constantly met with pushback by ZZZ2 whenever the East gate needs to be closed for weather. I do not understand why we let this Aircraft try to fly through a very large storm that was forming a dangerous horseshoe pattern when it was obviously dangerous for them and they almost lost complete control of their aircraft. Someone is going to lose their life because we keep sacrificing safety to get a few more planes out of the gate. ZZZ2 should work more closely with the weather department to predict when holes will fill in and try to anticipate losing gates rather than us literally letting planes fly into weather until someone cant get through and a dangerous situation develops.