  We employ Bayesian Model Averaging (BMA) as a powerful statistical framework
to address key cosmological questions about the universe's fundamental
properties. We explore extensions beyond the standard $\Lambda$CDM model,
considering a varying curvature density parameter $\Omega_{\rm k}$, a spectral
index $\mathrm{n}_{\rm s}=1$ and a varying $n_{\rm run}$, a constant dark
energy equation of state (EOS) $w_0$CDM and a time-dependent one $w_0w_a$CDM.
We also test cosmological data against a varying effective number of neutrino
species $N_{\rm eff}$. Data from different combinations of cosmic microwave
background (CMB) data from the last Planck PR4 analysis, CMB lensing from
Planck 2018, baryonic acoustic oscillations (BAO) and the Bicep-KECK 2018
results, are used. We find that the standard $\Lambda$CDM model is favoured
when combining CMB data with CMB lensing, BAO and Bicep-KECK 2018 data against
$K-\Lambda$CDM model $N_{\rm eff}-\Lambda$CDM with a probability $> 80\%$. When
investigating the dark energy EOS, we find that this dataset is not able to
express a strong preference between the standard $\Lambda$CDM model and the
constant dark energy EOS model $w_0$CDM, with an approximately split model
posterior probability of $\approx 60\%:40\%$ in favour of $\Lambda$CDM, whereas
the time-varying dark energy EOS model is ruled out. Finally, we find that the
CMB data alone show a strong preference for a model that includes the running
of the spectral index $n_{\rm run}$, with a probability $\approx 90\%$, when
compared to the $n_{\rm s}=1$ model and the standard $\Lambda$CDM. Overall, we
find that including the model uncertainty in the considered cases does not
significantly impact the Hubble tension.
