The dynamic properties of a biased two-level system in contact with a dissipative bath are studied in the weak coupling limit using a resolvent expansion method. The theory yields consistent results at low temperatures, a regime in which the widely used dilute bounce gas approximation (DBGA) to an underlying functional integral expression breaks down. The present results are however equivalent to a recently adapted functional integral technique that goes beyond the DBGA. The calculated expressions are relevant for analyzing the neutron scattering data on tunneling of light interstitials, e.g., hydrogen, in metals, at very low temperatures.