Why are intramolecular hydrogen bonds weaker than intermolecular hydrogen bonds?
I don't think there is much of a difference between the strengths of intramolecular or intermolecular hydrogen bonds.
However the strength of interactions between molecules depends on the type of hydrogen bond.
Consider a typical example: ortho-Nitrophenol has a lower melting and boiling point than para-Nitrophenol.
The interactions between molecules are much stronger when there are intermolecular hydrogen bonds (as in para-Nitrophenol) because the bonds are formed between molecules. This results in more stability and lower melting and boiling points (which might appear to be because of stronger bonds) because the molecules prefer to be closer to each other.
If intramolecular hydrogen bonds are present (as in the case of ortho-Nitrophenol) the interactions within individual molecules are greater and so there is less attraction between molecules. This causes less stability and higher melting and boiling points because the molecules are not really attracted to each other much and not because the hydrogen bonds are weaker.
It is mainly due to kinetic motion in molecules
The kinetic energy of molecules follows the Boltzmann distribution. Therefore, at room temperature molecules are constantly moving.
Intermolecular interaction, such as intermolecular hydrogen bonding only take place for a short time when two molecules are in each other's vicinity. Shortly after, the molecules separate and the interaction does no longer exist.
Intramolecular interactions on the other hand are much stronger since the two atoms forming the hydrogen bond remain in each others proximity due to structure of the molecule. In other words, they exhibit strain.