Lewis Acidic Strength Order:
$$\text{BI}_3 > \text{BBr}_3 > \text{BCl}_3 > \text{BF}_3$$
Back Bonding Concept: Boron is $$sp^2$$ hybridized with a vacant 2p orbital. In $$\text{BF}_3$$, effective $$p\pi-p\pi$$ back-bonding occurs from filled $$2p$$ orbitals of F to the vacant 2p orbital of B due to matching atomic sizes ($$2p\text{--}2p$$). As halogen size increases ($$\text{BF}_3 \to \text{BI}_3$$), orbital overlap efficiency drops ($$2p\text{--}3p, 2p\text{--}4p, 2p\text{--}5p$$), decreasing back-bonding strength and increasing Lewis acidity.