Ought we say 'body mass', rather than 'body weight'? I'm asking in the context of medicine, where you're "massed" (or is it "weighted"?) on a scale.
This answer beneath insinuates that 'mass' may be the preferred term, but it doesn't outwardly clarify if 'body weight' is wrong and ought be replaced by 'body mass'.

So why don't we call it "mass"? Well, according to
  http://www.etymonline.com/index.php?term=weigh, "weight" is a very old
  word, 

The original sense was of motion, which led to that of lifting, then to that of "measure the weight of." The older sense of "lift, carry"
    survives in the nautical phrase weigh anchor.

Before Newton, the concept of inertia didn't exist; so the distinction
  between mass and weight made no sense when the word was first
  introduced. And we stuck with it...

 A: There's nothing wrong with "body weight". In fact, most scales work by measuring the force you exert on them, so weight is actually more correct than mass. 
Of course, that means that scales that output in kilograms are lying a little; they're doing an implicit unit conversion that only works in standard gravity. But mass and force are always a complete mess. For example, in the imperial system there are 5 different definitions of the unit "pound". Some of them are masses (for which the corresponding force is a "pound-force"), some of them are weights (for which the corresponding mass is a "slug"), and some of them are both. So I can't even say for sure whether a scale in imperial units is lying or not.
I don't want to rehash the hundreds of conversations already had on this site about mass versus weight. We all already know the difference, and it's not a deep or really important one. Maybe some picky teacher will give you a zero over it, but in the real world, nobody cares!
A: Actually, the typical medical office scale (!) directly determines a moment of weight, or torque. A patient's weight is applied at some small $\perp$ distance, $r_p$ from a pivot. Masses are adjusted along an arm attached to the same pivot to balance the net torque to zero:
$$m_{\mathrm{patient}}gr_{p}=m_1gr_1+m_2gr_2+m_3gr_3,$$
where $m_1,~m_2,~\text{and}~m_3$ are the adjustable masses and arm used to balance th torque.  The arm is calibrated in terms of either mass units or equivalent earth-based weight units assuming a net zero torque about the pivot.  Because the  same gravitational field is affecting the all the masses, this scale would give correct mass measurement in any gravitational field, but wouldn't work at all in the ISS.
While weighing is the general non-technical term used, massing wouldn't apply to this scale.  Torquing the mass (or weight) would, pedantically, be correct, but I believe "scaling the mass" would be the most appropriate technical name for the process using almost any device, whether balance/torque-, spring-, or strain-gauge-based.
Socially, one shouldn't be a jerk, insisting that people quit using the verb "weigh." Smile and move on.
