${\mathrm{AlCl}}_3$ dimerises while ${\mathrm{BCl}}_3$ does not because

Both BCl₃ and AlCl₃ are electron deficient but in BCl₃, there is back bonding which is not occurred in AlCl₃ because of large size of Al. In BCl₃, there is $p\mathrm{\pi }-\mathrm{p\pi }$ back bonding between 3p orbital of Cl and 2p vacant orbital of B but due to large size of Al, there is no effective overlapping takes place between 3p orbital of Cl and empty orbital of Al. Therefore, it undergoes dimerization to stabilized itself.