Raising taxes may be a bad thing to bring to a policital campaign, but inventing a new tax for the state is electoral death. The general concensus at the time was that Weicker was so pissed at being kicked out of the Senate, he created his political party and orchestrated his independent win in the governor's race for the sole purpose of instituting a state income tax, and saying a big fuck you to the people of Connecticut. Of course he did not run for a second term, and has not run for election since then.
Lieberman can definately be beat in a primary, but he can not be beat by Weicker. Hell, I dont think Weicker could beat me.