Question: Most people say that it is because the 3p orbital of chlorine when overlapping with the s orbital of hydrogen covers more area than when 4p orbital of bromine overlaps with the s orbital of hydrogen which makes bond between H and Cl more stronger than the bond between H and Br. But how can we say that the area of overlapping is more for 3p and s orbital compared to overlapping of 4p and s orbital?

Answer: 
You can think of the overlapping volume between the electron clouds, but a simpler form to show why this happens is when you consider the electrical potential between the atoms. Even tough this isn't an ionic compound, it has many characteristics that are similar. 

If I remember correctly, this is the expression for the potential energy between charged particles: $E\_p = k\frac{Q\_1 \cdot Q\_2}{d}$

Since the radius of $\ce{Br}$ is greater than the radius of $\ce{Cl}$, the potential energy involved in $\ce{H-Br}$ bond will be smaller than $\ce{H-Cl}$ bond.

Another thing that came to my mind, and I'm not sure, is that as the 4p cloud of $\ce{Br}$ is bigger than that of $\ce{Cl}$, the relative amount of the volume that is overlapped with the 1s cloud of $\ce{H}$ gets smaller with $\ce{Br}$ than with $\ce{Cl}$, which means the connection is weaker.
If you aren't convinced by the overlap area argument, then think of it in terms of polarization. The H+ cation will polarize Br- more as compared to Cl-, so HBr will possess a more covalent character as compared to HCl, or conversely, H-Cl bond will be more ionic than the H-Br bond. And as we know, ionic bonds are generally stronger than covalent bonds