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In the framework of general relativity (GR), gravitational waves (GWs) travel at the speed of light across all frequencies. However, massive gravity and weak equivalence principle (WEP) violation may lead to frequency-dependent variations in the propagation speed of GWs, which can be examined by comparing the theoretical and observed discrepancies in the arrival times of GW signals at various frequencies. This provides us with an opportunity to test these theories. For massive gravity, we consider that gravitons may have a nonzero rest mass. For WEP violations, we hypothesize that different massless particles exposed to the same gravitational source should exhibit varying gravitational time delays. The gravitational time delay induced by massive gravitational sources is proportional to $γ+1$, where the parameter $γ=1$ in GR. Therefore, we can quantify these two deviations using phenomenological parameters $m_g$ and $|Δγ|$, respectively. In this study, we use selected GW data from binary black hole coalescences in the LIGO-Virgo catalogs GWTC-2.1 and GWTC-3 to place constraints on the parameters $m_g$ and $|Δγ|$. We analyze the relationship between $m_g$ and luminosity distance,as well as between $|Δγ|$ and both luminosity distance sky location of GW events to determine the presence of graviton mass and WEP violation. Nevertheless, we find no evidence of such relationships. We also compute Bayes factors for models that assume the existence of graviton mass and WEP violation compared to the standard GW model, respectively. The absolute value of the natural logarithm of the Bayes factor is generally less than 2. Our analysis reveals no significant preference for either model. Additionally, the Bayes factors between these two models do not provide obvious evidence in favor of either one.