"Does paraffin dipping make boxes heavier?"

As Peter Edwards says, there would be some weight reduction through the
driving off of the moisture in the wood - I'm not sure if that has ever been
quantified.

My beekeeper's 'ready reckoner' at http://www.beekeeping.co.nz/convert.htm
includes the "rule of thumb" that you need about 16.6 kg of paraffin to
treat 100 full depth boxes - that would equate to 166gm per box - just under
6 oz per box...

I'd reiterate the importance of the wax temperature (for both preservation
and disease treatment) to avoid the 'wax envelope' effect.  When done
correctly, you can't feel the wax on the surface...

Nick Wallingford
Tauranga, NZ
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http://www.beekeeping.co.nz