I agree the weight of the stove itself is a consideration for trim and draft, although I doubt it's as heavy as you think (I'll find out Saturday morning, when I load it into my pickup).
I know these types are not heavy by “whole” house measurements, as a standard. But you’re on a small boat. Thus the key to this is the stability, in terms of the trim/list (especially if not on the centreline) and the statical stability.
If you don’t have one already, you’re best to get a set of hydrostatics of the hull from lightship to full load (or anticipated max DWL). Then you can see if the heavy weight will influence what else you can have onboard and how high up will be safe. Since whist the burner may not be heavy per se, yet, in terms of the boat and what it displaces and with a shallow draft and narrow-ish beam, its weight can be 'considerable' especially if too high, and the last thing you want is a wave to pass you and the boat flops over to an angle of lol, or worse, over, owing to poor intact stability.
