This paper studies a cognitive or secondary multi-antenna wireless power transfer (WPT) system over a multi-carrier channel, which shares the same spectrum with a primary wireless information transfer (WIT) system that employs adaptive water-filling power allocation. By controlling the transmit energy beamforming over sub-carriers (SCs), the secondary energy transmitter (S-ET) can directly charge the secondary energy receiver (S-ER), even purposely interfere with the primary WIT system, such that the primary information transmitter (P-IT) can reactively adjust its power allocation (based on water-filling) to facilitate the S-ER's energy harvesting. We investigate how the secondary WPT system can exploit the primary WIT system's reactive power allocation, for improving the wireless energy harvesting performance. In particular, our objective is to maximize the total energy received at the S-ER from both the S-ET and the P-IT, by optimizing the S-ET's energy beamforming over SCs, subject to its maximum transmit power constraint, and the maximum interference power constraint imposed at the primary information receiver (P-IR) to protect the primary WIT. Although the formulated problem is non-convex and difficult to be optimally solved in general, we propose an efficient algorithm to obtain a high-quality solution by employing the Lagrange dual method together with a one-dimensional search. We also present two benchmark energy beamforming designs based on the zero-forcing (ZF) and maximum-ratio-transmission (MRT) principles, respectively, as well as the conventional design without considering the primary WIT system's reaction. Numerical results show that our proposed design leads to significantly improved energy harvesting performance at the S-ER, as compared to these benchmark schemes.