It sure does. But we have to consider that recharging is less efficient than not spending the energy on acceleration in the first place, so heavier EVs are worse off than lighter ones; it’s not only losses from friction and heat losses - those come on top.
And you’re spot-on with the danger that comes from weight; being in an accident with a lot of kinetic energy that needs to be absorbed is not great.

I was comparing EVs with different weight and not comparing EVs with ICE vehicles, though.
And in that case the heavier EVs are less efficient than more leightweight versions even with regenerative breaking, because the process of accelerating and breaking cant’ regenerate all energy that was spent for accelerating.

That’s not that big of a deal for long-range trips, on which you typically don’t have to accelarate often.
Keeping the car going at a certain speed depends on several types of resistance, most importantly air resistance, but not really on weight.
More weight plays a bigger role for energy consumption in urban ares, where the weight needs to be accelerated more often than on the highway, the mileage per kWh is yet typically higher than on the highway due to the lower speed and less air resistance.
What I’m trying to say: I’d pick the bigger battery any time over the smaller one, if the price is reasonable.
EVs are already heavy. The weight from some additional batteries don’t play a big role.