I don't remember if it was a previous chapter, or one of the novel versions that goes into more detail - but MC is not "pro slavery", but very much understanding of why it exists in this world, and just how difficult it would be to abolish as a practice.
As in - looking at just IRL USA history, a literal war was fought over it. And the ramifications still echo through the country's history into the present.
He lays out some of it here - he's just annoyed at the empty idealism and vacuous platitudes that Allen expresses, because it's really easy to say "[Thing] is bad", when you're not also following that statement up with meaningful steps to actually walk that talk.
He is on the record somewhere as thinking slavery is abhorrent, but he's also considering just how immense tackling the removal of that system would be, given the uphill battle of facing off against all of the nobility that not only relies on, but economically thrives on it - the situation of all the people formerly in bondage, the actual economic impact that would have to be addressed - both in terms of the removal of that labor pool, but also the money to pay them to work, the housing, clothing, food, medical care, and more they would all require, and so on.
And he also acknowledges that, in some senses, children put into bondage who've lost their families to war, abandonment, famine/disease and so on, are given some modicum of stability and material guarantee, if not comfort. It's clearly not good, but for the present moment, it means they're not on the streets either dying or resorting to violence and theft, creating downstream issues for society at large.
TL;DR Weiss is super pragmatic about the realities of it while being personally against it; Allen is 100% emotion and idealistic rhetoric but offers zero actionable solutions.
But it would seem that, where Allen is concerned, the OG Weiss is more prone to coming to the surface than normal, and in ways MC can't always anticipate and control.