To explore the potential of field-effect transistors (FETs) based on monolayers (MLs) of the two-dimensional semiconducting channel (SC) for spintronics, the two most important issues are to ensure the formation of variable low-resistive tunnel ferromagnetic contacts (FCs) and to preserve intrinsic properties of the SC during fabrication. Large Schottky barriers lead to the formation of high resistive contacts, and methods adopted to control the barriers often alter the intrinsic properties of the SC. This work aims at addressing both issues in fully encapsulated ML WSe2 FETs using bilayer hexagonal boron nitride (h-BN) as a tunnel barrier at the FC/SC interface. We investigate the electrical transport in ML WSe2 FETs with the current-in-plane geometry that yields hole mobilities of similar to 38.3 cm(2) V-1 s(-1) at 240 K and on/off ratios of the order of 10(7), limited by the contact regions. We have achieved an ultralow effective Schottky barrier (similar to 5.34 meV) with an encapsulated tunneling device as opposed to a nonencapsulated device in which the barrier heights are considerably higher. These observations provide an insight into the electrical behavior of the FC/h-BN/SC/h-BN heterostructures, and such control over the barrier heights opens up the possibilities for WSe2-based spintronic devices.