  We study theoretically laser excitation of Rydberg triplet states of
strontium atoms in the presence of weak microwave (MW) fields. Starting from
the ground state $5s^2\,^1S_0$, the Rydberg excitation is realized through the
metastable, triplet $5s5p\,^3P_1$ state, whose decay rate $\gamma_2$ is
$2\pi\times 7.5$ kHz, much smaller than the one in the singlet state or alkali
atoms. The influences of $\gamma_2$ on the transparency and absorption spectrum
in the electromagnetically induced transparency (EIT), and electromagnetically
induced absorption (EIA) regime are examined. Narrow transparent windows (EIT)
or absorption peaks (EIA) are found, whose distance in the spectrum depends on
the Rabi frequency of the weak MW field. It is found that the spectrum exhibits
higher contrast than using the singlet state or alkali atoms in typical
situations. Using the metastable intermediate state, we find that resonance
fluorescence of Sr gases exhibits very narrow peaks, which are modulated by the
MW field. When the MW field is weaker than the probe and control light, the
spectrum distance of these peaks are linearly proportional to $\Omega_m$. This
allows us to propose a new way to sense very weak MW fields through resonance
fluorescence. Our study shows that the Sr triplet state could be used to
develop the Rydberg MW electrometry that gains unique advantages.
