This is my view for what it’s worth;
Your bat is constantly being subjected to something known as Equilibrium Moisture Content (EMC).
From Wikipedia: “The moisture content of wood below the fibre saturation point is a function of both relative humidity and temperature of surrounding air. The equilibrium moisture content (EMC) is the moisture content at which the wood is neither gaining nor losing moisture; this however, is a dynamic equilibrium and changes with relative humidity and temperature.”
This basically means that the bat is always trying to be in equilibrium with its current environment whatever that may be. In this country during the summer EMC (outside) will be approximately 15% rising to 20% in the winter. Bring your bat indoors to a centrally heated house and this can be as low 6%. In India EMC outside can drop as low as 6% in the summer but will average around 10%. Obviously this is why bats coming out of Asia are so much dryer. Typically, finished bats have a moisture content of around 10-12% as we all know, which is below the EMC of a typical British summer. If we did not seal the bat with a water proof layer (linseed, bees wax) the bat would always want to absorb moisture even in very dry conditions. Contrary to popular belief (or so it would seem) linseed does not add any moisture to your bat although it will soften the fibres that are in contact with the oil which is where I think some of the confusion occurs.
Doing some simple sums;
Typical volume of modern bat blade = 0.0024m^3
Density of willow (approx.) 420 Kg/m^3
Blade weight = 0.0024 * 420 = 1.008kg -> 2lb 35oz
Add to that 6-7oz for the handle and you end up with a bat in the region of 2lb 10oz
I don’t really believe that variations of 2% in moisture content have much of an impact on overall bat weight. If you do a quick calculation, 2% of a typical bat weight is less than an ounce. The weight will be affected by the willow density though and as willow can vary in density from 350 – 450 Kg/m^3 this could lead to a variation in blade weight (minus the handle) of 2lbs - 2lb 6oz.