In this paper, we examine the consistency of the Large Hadron Collider (LHC) data collected during Runs 1 and 2 by the ATLAS and CMS experiments with the predictions of a 2-Higgs doublet model embedding vectorlike quarks (VLQs) for pp -> H, A production and H, A -> gamma gamma decay mechanisms, respectively, of (nearly) degenerate CP even (H) and CP-odd (A) Higgs bosons. We show that a scenario containing one single VLQ with electromagnetic charge 2/3 can explain the above ATLAS and CMS data for masses in the region 350 GeV <= m(VLQ )<= 1.5 TeV or so, depending on tan beta, and for several values of the mixing angle between the top quark (t) and its VLQ counterpart (T). We then perform a global fit onto the model by including all relevant experimental as well as theoretical constraints. The surviving samples of our analysis are discussed within 2 sigma of the LHC measurements. Additionally, we also comment on the recent anomalous result reported by CMS using Run 2 data on the associated Standard Model Higgs boson production with top quark pairs pp -> t(t)over-barh with an observed significance of 3.3 sigma. Other than these specific examples, we also present a phenomenological analysis of the main features of the model, including the most promising T decay channels.