Dispatcher voiced concern regarding lack of staffing during IFR weather conditions; noting management's reluctance to call out overtime.

Narrative

The DSC will observe the weather/operations and if they anticipate possible irregular operations they would advise management. Management has the task of ensuring enough qualified dispatchers are at the dispatch center to [provide] proper operational control of each flight. Upon review [of]enroute weather and destination weather throughout the East Coast I noticed that the National Weather Service was forecasting low IFR condition and thunderstorms for the greater part of the day from TPA/MCO/ATL/MYR/DCA/ACY/LGA/BOS and throughout Northern FL; GA; thru NY; MA. With our current staffing; Dispatch has [a] problem flight following our aircraft and updating our flights with weather that may affect the safety of flight. On VFR days we are adequately staffed; we need help to properly maintain Operational Control [during low weather operations]. Suggestion: the night shift coordinator should request an additional dispatcher due to possible irregular operation because of forecasted low IFR conditions and thunderstorms. Nothing was done from Management except to wait for an irregular to happen. We need proper written guidance from management/FAA/Dispatch Group on when we call out for an additional dispatcher without considering overtime vs safety of flight and flight following.