Does the unbelief of Jesus' brothers support Mary's perpetual virginity?

I recently heard somebody make that claim. If Jesus' brothers grew up in the same house as Jesus, which would have included having a large amount of information about or even witnessing miracles associated with him, for example, why weren't they believers?

That's just a variation of an objection that's been raised for a long time in other contexts. See my response to Raymond Brown's formulation of it here and here and my response to Bart Ehrman's version of it here, for instance. There's no reason to think there were as many or more miracles occurring in association with Jesus in his home prior to his public ministry than during that ministry. But his brothers were unbelievers during that latter timeframe. The typical non-Christian argument pertaining to Jesus' miracles at the time wasn't that there weren't any miracles, but rather that they didn't come from God. It wasn't an absence of miracles that was motivating the unbelief.

And though children of Joseph from a previous marriage and cousins would be further removed from Jesus than children born from Mary, we'd still expect children from a previous marriage and cousins to have had a lot of contact with Joseph, Mary, and Jesus. Look at how often they're in close proximity to Jesus and Mary in the gospels and elsewhere. That probably occurred prior to Jesus' public ministry as well. Just as there isn't much difficulty in reconciling the unbelief of Jesus' brothers with their being step-brothers or cousins, there isn't much difficulty in reconciling their unbelief with their being brothers in the most common sense of that term.

Distancing the brothers from Jesus makes their unbelief less difficult to explain in some ways, but not in every context. If the brothers were children from a previous marriage, then they lived through the events of the infancy narratives, as Joseph and Mary did. By contrast, children later born from Mary didn't. Children from a previous marriage also would have been more mature during Jesus' childhood, more capable of handling evidential contexts like having conversations with Joseph and Mary about the relevant issues. In some ways, the unbelief of Jesus' brothers is easier to explain if they were children born from Mary after Jesus' birth or cousins born later rather than earlier.

Even if somebody concludes that a perpetual virginity scenario offers a better explanation of the brothers' unbelief, I don't think it would be much of an advantage. As I said in an earlier post, an advantage for a particular view of the brothers in one context can be accompanied by a disadvantage in another context. What we're after is the best explanation of the evidence as a whole. As the post just linked argues, the view that Mary gave birth to other children is the most efficient explanation on balance, even though it's not the best explanation of every piece of evidence. A Joseph who was older at the time of his marriage to Mary better explains his death prior to Jesus' public ministry, and the perpetual virginity view was held by more of the church fathers, for example, but the advantages of a perpetual virginity view are accompanied by more numerous and weightier disadvantages.