Bluetooth Low Energy (BLE) is one of the most popular wireless protocols for building IoT applications because of its low energy, low cost, and wide compatibility nature. However, BLE communication performance can be easily affected by interference and blockages because of its low transmission power. This paper presents BLEW, a technique to improve the BLE communication performance over weak links by exploiting adaptive symbol extension and DNN-based demodulator to combat channel interference and maximize network throughput. First, we propose a phase peak clustering-based preamble detection method that coherently adds up the phase difference of preambles to combat the interference. We then propose a multi-domain DNN-based demodulator to fully extracts the temporal and spectrum features of the signal and enhance the demodulation performance. Finally, we model the throughput of Commercial Off-The-Shelf (COTS) BLE chips transmitting extended packets, which can be used to optimize the symbol length in an adaptive manner. We implement BLEW with USRP B210 and COTS nRF52840 platform. Experiments show that BLEW can increase throughput by up to 157.39 Kb/s compared with native BLE over typical weak links. Compared with existing approaches, BLEW has up to 25.70% higher preamble detection rate and up to 3.37 dB demodulation gain.