The $\mathrm{F}-\mathrm{F}$ bond is weak because 

The bond length of $\mathrm{F}-\mathrm{F}$ bond is much larger than the bond length in other halogen molecules.

The $\mathrm{F}-\mathrm{F}$ bond distance is small and hence the inter nuclear repulsion between the two ‘F’ atoms is very low

The ionization energy of the fluorine atom is very low 

The repulsion between the non bonding pairs of electrons of two fluorine atoms is large