Maximizing network throughput while providing fairness is one of the key challenges in wireless LANs (WLANs). This goal is typically achieved when the load of the access points (APs) is balanced. Recent studies on operational WLANs, however, have shown that AP load is often substantially uneven. To alleviate such imbalance of load, several load balancing schemes have been proposed. These schemes commonly require proprietary software or hardware at the user computers for controlling the user-AP association. In this paper we present a new load balancing technique by controlling the size of WLAN cells, which is conceptually similar to cell breathing in cellular networks. The proposed scheme does not require any modification at the user side neither the standard, but it only requires the ability of dynamically changing the transmission power of the AP beacon messages. We develop algorithms that find the optimal beacon power settings, which minimize the load of the most congested APs, in polynomial time. We also consider the problem of network-wide min-max load balancing. While this problem is NP-hard and cannot be easily approximated, we identify a variant of the problem, termed min-max priority load balancing, and present polynomial-time algorithms to find optimal solutions. Extensive simulations show that the performance of the proposed method is comparable with or superior to the existing association-based methods.