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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 $γ_2$ is $2π\times 7.5$ kHz, much smaller than the one in the singlet state or alkali atoms. The influences of $γ_2$ 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 $Ω_m$. 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.