The Lewis acid character of boron trihalides depends on the extent of $p\pi-p\pi$ back bonding. In $BF_3$, the fully filled 2p orbital of fluorine effectively overlaps with the vacant 2p orbital of boron, significantly reducing boron's electron deficiency. As the size of the halogen atom increases down the group ($2p$ for F, $3p$ for Cl, $4p$ for Br), the orbital overlap between its filled p-orbital and the empty 2p orbital of boron becomes progressively weaker and less effective due to the size mismatch. Consequently, the electron deficiency of the central boron atom is least compensated in $BBr_3$ and most compensated in $BF_3$. Therefore, $BBr_3$ is the strongest Lewis acid, and the correct decreasing order of Lewis acidic strength is $BBr_3 > BCl_3 > BF_3$.