Could a larger block size increase the security of the block cipher? I want to know if a larger block size increase the security of the block cipher?
TL;DR: a larger block size won't help to make the block cipher itself more secure, but it can be used to make the schemes using the block cipher more secure.

The block size basically determines the number of possible permutations: the possible ways to combine all the possible plaintext blocks with the possible ciphertext blocks. The number of permutations grows much faster per bit of the block size than the number of possible keys from the key size. In that sense it is unlikely that a larger block size will do much for the security of the cipher.

Modes of operation however do rely on the block size for other purposes. For instance, the counter size of AES-CTR is defined to be the same size as the input block size. That counter usually consists of a random nonce and a counter part, for instance 64 bits for the nonce and 64 bits for the counter. However 64 bits is not that much for a nonce; as the birthday problem applies you can only encrypt about $2^{32}$ ciphertext before the counter could repeat. Now this isn't a huge problem, but it would be avoided with a block size of 256 bits (or, indeed a tweak, or both).

Specific constructions could also require a larger block size. For instance a hash function generally relies on large state. To go from one large state to another a block cipher could be used. Obviously it would need to have a large state and a large block size itself. There are other ways to do this with a cipher with a smaller block size but it won't be as efficient.