ZFW Controller expressed concern regarding the unwillingness of traffic management to re-route traffic over MEM as requested by the flight crew due to weather; reporter suggesting improved response to pilots weather routing needs.

Narrative

Thunderstorms were present toward ATL and an in-trail requirement of 40 NM was in place over MEM. Aircraft X checked on my frequency and advised that he had been assigned MEI HONIE5 ATL and that he needed to go back over MEM ERLIN5 ATL due to weather to the southwest of ATL. Aircraft X was about 60 miles behind Aircraft Y and 20 miles in front of Aircraft Z; if they were all going to MEM (as the other two were). There was also Aircraft W 65 miles behind Aircraft Z. I advised the pilot he was on a TMU (Traffic Management Unit) Reroute and I would relay his request. I advised FLM who called TMU; and then told me unable. I relayed this to the pilot of Aircraft X. About 3 minutes later; Aircraft X called again and said after talking to his dispatch that though his dispatch 'would allow us to go over MEI' that he still needed to go over MEM. I relayed this to FLM (Front Line Manager); who again called TMU. This time the response was 'unable due to in-trail requirements'. Aircraft X; when advised of this; asked what the 'third plan was?'; I told the pilot that there was not one at this time and I would again relay his concerns. I then spoke to FLM again and after that he advised me to switch Aircraft X to DECOD-HIGH and that they would fix it and put Aircraft X back over MEM. I did so; and they did too. Recommendation; we have to listen to pilots. Weather concerns are a current focus and here we are telling a pilot to shut-up and fly the route we assigned you.