The Bond Dissociation Energies of these molecules are in the order
Cl2 > Br2 > F2 > I2
All these molecules involve a single covalent bond. Covalent bonds rely on sharing of a pair of electrons between two atoms, an electron each from both atoms involved. The better the sharing, the stronger the covalent bond formed. This sharing is reflected in the valence shell orbital overlap that occurs between the two atoms, when a more effective overlap occurs, a stronger covalent bond is formed.
Now, the radii of the halogen atoms increases in the order of writing them down the group, F < Cl < Br < I < At. As the atoms get larger, so do the valence shell orbitals. The increase in size of orbitals carrying the same number of electrons would mean that the electron density would be lower in larger orbitals. So, for the same proportional overlap between two similar orbitals of similar atoms, the sharing of electrons would be poorer and would consequently result in a weaker covalent bond.
This should explain the strength of bonds decreasing as we go down the group.
However, in this orbital overlap consideration gets forgotten another factor that becomes important when atoms are small in size, and that is of electronic repulsions.
Fluorine is extremely small in size and so the electron density is pretty high as well. This results in an unstable arrangement if the atoms come too close, since like charges repel.
The interplay of the above mentioned effects results in Chlorine having the highest bond strength.
I may also add that the same is the case for (1) N-N bond energy as against P-P bond energy and (2) O-O bond energy as against S-S bond energy. But, do keep in mind this stands true only for single bonds.