implication of tweak on bruteforcing a block cipher
The tweak is generally not secret, i.e. the adversary knows it (perhaps even chooses it, depending on the attack model) and thus doesn't have to try to guess it.  So no, tweaks don't increase the effort to brute force a cipher ... unless of course the tweak is kept secret, in which case it may or may not increase the required effort, depending on how the tweak is mixed into the cipher state.