What does a tonearm contribute to the sound of a turntable?

Very important to the overall sound.

I agree with ebm - one of the biggest upgrades I have made was a great tonearm - 
Basis Vector 4 for my Basis table.

hi,
20-30% (at most), most important part is the turntable itself, a stable platform is the foundation. 

Tonearm must provide a stable platform for the cartridge to function optimally. The corollary is that specific tonearm/cart combo matters greatly for sound quality.   Cartridge compliance specs help determine tonearm mass needed for good performance.  Mass and rigidity are two key attributes. In general you want to optimize the electric signal transfer from the stylus as it modulates while tracking the record groove. Tonearm provides the platform for the stylus to move and perform that function accurately.

I have a version of damping tape on the drivers in my Spatials. Their previous owner put it on and said it really helped control the sound. I took his word for it.

A few more things:

1. I'm going to re-drill my armboard; I'm off by 3.5mm on my Feickert and when I used Stevenson alignment, I feel the connector wires from the head shell to the cartridge are too smushed together.
   
2. I conducted a decibel test using the Ultimate Analogue Test LP left and right azimuth and found that my right speaker tests about 10 decibels higher than my left. Yet when playing Dire Straits' BIA 45 reissue and comparing with with the SACD, the instruments were in their correct channels and had comparable loudness levels. Waddup with that? I plan on swapping tubes on my Pathos tonight to see if that's the culprit.
   

Btw - everyone's advice and straightforward info is much appreciated.