Covalent bond nature in electronegativity gap Does a large difference in electronegativity mean the covalent bond is weaker?


In a covalent bond between two atoms of different electronegativities, the bonding electrons are pulled towards the more electronegative electron. This makes the bond polar (eg. $HCl$).

In a diatomic molecule, the electronegativity is the same so the electrons are equally attracted to either atom. Does this make diatomic covalent bonds stronger than the former? And if so, as the difference in electronegativity increases, does the strength of the covalent bond decrease?
Strength of covalent bond depends on many factors, one of the key factors is "extent of overlapping of orbitals". For e.g., if you consider $\ce{H2}$ molecule, there is a head on overlapping of $\mathrm{1s-1s}$ orbitals involving two hydrogen atoms, but in the case of, say, $\ce{HCl}$, there is a head on overlapping of $\mathrm{1s-3p_z}$ orbital ($\mathrm{1s}$ of hydrogen, and $\mathrm{3p_z}$ of chlorine), and we all know that $\mathrm{p-s&gt;s-s}$, that is, overlapping between a $\mathrm{p}$-orbital and a $\mathrm{s}$-orbital is stronger than $\mathrm{s}$ and  $\mathrm{s}$ orbital, and stronger the overlapping more is the covalent bond energy.

So, it largely depends on the type of orbitals involved and the nature of overlapping. 

Check this to learn more about overlapping.