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Adding one bit mostly means the number of decoded possibilities is twice as large. Adding two bits increases the space by a factor of four (i.e., by 2^2). Adding 128 bits increases the decrypted data space by a factor of (2^128) or by a factor of (3.4028236692093846346337460743177e+38) according to the Windows calculator.
A 128 bit key is 16 bytes, and 256 bits is only 32 bytes. The key size isn't enough to be a significant factor in itself, but the expanded potential resulting data space is astronomical at least, especially when compared to 128 bits.
It's a lot more time consuming to crack for a relatively small increase in key size.