We've had that problem for more than a century, as did most of the Euro states that held overseas terrain and spheres of influence. Stability so you can forget their local issues is too attractive, and most decision making too short term in orientation to take the more difficult path.
And as to poor, weak, and unstable....we tend to like stable but militarily weak as they make better trading partners and non-threats (course weak and stable don't cohere well so...). We also don't require them to be poor, we're in it for what we can get out of it. Doesn't necessarily have to be at their expense, though that has often been the case.
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