A Center Controller reported during a period of aircraft weather deviations into one sector no action was taken by Management or Traffic Management Unit (TMU) staff to reroute aircraft away from the sector causing it to exceed the designated maximum safe traffic numbers for that sector.

Narrative

While working R35 I observed the traffic building and several red numbers approaching on the TSD (Traffic Situational Display) board for R52. Weather was building and at least 2 large MOAs were active. All of our sectors were already split as much as possible. I notified Controller in Charge (CIC) of the problem and the CIC notified Traffic Management Unit (TMU) immediately. Front Line Manager (FLM) relieved CIC for break shortly after. It seemed that nothing had been done to alleviate the approaching red blocks. I notified FLM about the situation and asked if he had already done everything possible to slow the traffic down. I volunteered to call W35 and W09; since R52 was already getting busy; and have them route a few aircraft west over the coastline. FLM said 'it was fine'. I told him it was about to get bad and this was our only chance to fix it. He said 'turn around and face my scope'.I was surprised at the apathy but I did as told. I don't know if any further action was taken. I was relived for break shortly thereafter and briefed my relief that R52 was about to be very busy and to help however possible. I remarked to R51 that I was surprised nothing was being done. He wasn't surprised and said that the same thing happened yesterday. When I returned from break R52 with a Dside was completely down the toilet with traffic; weather; and JAINS deviations. The TSD was showing 4 blocks of solid red and the rest yellow with numbers from 28-35. The maximum for R52 is 23 under ideal conditions. I couldn't count all the aircraft but I would estimate that he had nearly 40 on his scope at one point. Most were deviating and asking for different altitudes. Half of his transmissions were 'standby; or unable requests'. A tracker was paged back from break. It took over an hour to stabilize the sector. R35 also noted what a mess it was.I've seen plenty of sectors get too busy or unsafe in my career. This was; however; the most easily preventable situation I've seen. R47/48 were combined the entire time because they were slow. 5-10 aircraft could've been routed through their space every half hour and would have been easily managed. I'm not sure if TMU took any action but it certainly wasn't enough. I was willing to call W35/W09 and ask them to climb anyone capable up to R51 and to route a few specific planes around R52 to prevent this. I was basically told to mind my own business and not to worry about it.