Timely processing of streams in parallel requires dynamic load balancing to diminish skewness of data. In this paper we study this problem for stateful operators with key grouping for which the process of load balancing involves a lot of state movements. Consequently, load balancing is a bi-objective optimization problem, namely Minimum-Cost-Load-Balance (MCLB). We address MCLB with two approximate algorithms by a certain relaxation of the objectives: (1) a greedy algorithm ELB performs load balancing eagerly but relaxes the objective of load imbalance to a range; and (2) a periodic algorithm CLB aims at reducing load imbalance via a greedy procedure of minimizing the covariance of substreams but ignores the objective of state movement by amortizing the overhead of it over a relative long period. We evaluate our approaches with both synthetic and real data. The results show that they can adapt effectively to load variations and improve latency efficiently comparing to the existing solutions whom ignored the overhead of state movement in stateful load balancing.