It's telling you that you're not pulling it from the same place on the string that your string hand will pull it from
... actually, that's more what it's telling ME, because when someone says a bow is rocking in the tree, before I respond, or judge the bow, I immediately look for... How/where is it being held? and how/where is it being drawn? and it appears that you're holding it and pulling it from its center.
If you pulled it from the 'correct' place on the string, it would act differently... in fact, it would almost have to tilt the OTHER way, as that particular bow should early in the draw... because.....
The second thing I check is whether the bow is designed with equal length limbs. It appears yours is. Such a bow, in the early draw, held and drawn as the archer will, will usually try to tilt the opposite way until it makes the shift from static balance to dynamic... assuming it IS dynamically balanced.(balanced for equal limb strain, relative to the archer's holds at his full draw)
My advice would be to set the bow in the cradle to reflect your BOW hand fulcrum point, pull it from the place on the string that best reflects your STRING hand fulcrum point, and THEN judge it. Until you do, judging it, and correcting it, is a guessing game at best.
To answer your question as it stands(because I can make a good point with it)... With the grip center as the bow fulcrum AND string fulcrum(which is how yours appears to be set up)... what the tilting is telling you is... the limb on the left is stronger(relative to those holds) than the limb on the right, because if a bow is allowed to rock or rotate in the cradle, as it's drawn the relatively stronger limb will be pulled down and the weaker limb will lift up... like Del described.
"It's supported and pulling on the center. So bottom limb (left) is a bit stiff. That's a good thing, right?"
No. Not necessarily. With all-wooden bows, predetermined braced profiles... i.e. 'tiller measurements', such as 1/8" positive tiller... "the bottom limb should be stronger", etc... are just guesses... at the very best. I don't know how to stress that strongly enough without cussing
Instead, hold them how you'll hold them, draw them how you'll draw them, and seek relative limb balance throughout their construction.
Achieving good relative limb balance can either be detected by using 'true holds' while allowing a bow to rock freely in the cradle, and then adjusting limb strength so that it doesn't...
OR, by holding it firm in the cradle, and adjusting relative limb strength so that the 'true' string fulcrum isn't pulled at all toward one limb or the other at full draw. With the grip held as such, if one limb is stronger than the other, the string fulcrum will always be pulled toward the relatively stronger limb.