Should tweak be unique per message? Since tweaks are like IV,Salt for block cipher inputs . Should they be unique for each message ?

If they are to be unique per message then what is the advantage of giving tweak directly into the message than giving IV ?

Edit : Is there a way in which we need not give unique tweak per message but get same security levels as giving unique IV per message ?  as there are many ways of providing a tweak .
Tweak per message offers good security like IV per message . 

Basically a tweakable block cipher with same tweak for all messages is same as non-tweakable block cipher. It is deterministic in nature and not considered secure enough in itself. You need to apply a mode of encryption that has been designed for non-tweakable block ciphers to make it secure.