[X] Azel
I want a stronger start to this conversation, but frankly, until we understand his motives, there's not too much we can do. We can either say "press your luck" and let him sink or swim, but that's a level of negligence for the fates of our neighbors (and thus our subjects by extension due to proximity) that we find intolerable, so our only recourse is to give him a slight advantage by pressing his terms first, then finding a way to match them while meeting our own concerns.
The main problem as I see it is that Braavos is only interested in Pentos insofar as it could release greater threats from its downtrodden populace and greedy magisters if left alone, but once they have control over it, it is more in their interests to downscale it into ignominy so that it can never rise to threaten their position ever again.
But this renders a population center and entire region into something propping up Braavos, the people leveraged to produce raw materials for Braavosi export. It doesn't actually benefit us.
Now take what we would do with the whole region. We would link it up to our roads. We would redevelop the city so that it retains all or most of its current size, but create more viable long-term industries, increase local trade and sponsor new businesses. This would lead, inevitably, to developing and exploiting the hinterland to provide for these industries, so more mines, more fields, and more mills, and so on.
Which means more taxes. Which is good for us.
Braavos hasn't ever focused or revolved around taxes beyond the context of trade duties, and they get better duties from their own port (and from trade deals, like what they have from us).
Targaryens understand taxes. Every great project they have undertaken, has been to the ends of increasing their piece of the pie that assessors collect. It's probably the one success of Aerys' rule, even if it had nothing to do with him. Thanks to our ancestors, Tywin found it trivially easy to make the royal treasury fit to burst with gold.