An article in the most recent PNAS by Gary Evans and Michelle Schamberg, "Childhood poverty, chronic stress, and adult working memory", argues that intergenerational transmission of poverty might be due to debilitating effects of childhood stress. The Economist provides a decent summary for those without PNAS subscriptions. The article finds that kids from low socioeconomic status backgrounds have shorter working memories than do their more affluent counterparts, and that childhood stress levels seem to do more in explaining working memory at age 17 than does duration of childhood poverty. Children with a higher allostatic loading have worse working memory when older than do others. Once allostatic load is taken into account, income no longer has explanatory power.
Nowhere does the study seem to correct for parental IQ. We have reasonable evidence that IQ and working memory correlate, though there is some debate. We also have reasonable evidence that IQ is highly heritable. Finally, we have good evidence that IQ correlates with health outcomes. Let's put that all together then. Low parental IQ transmits directly to children. At the same time, low parental IQ generates lower income households and poorer health outcomes. These health outcomes get measured as allostatic loading. Blood pressure and BMI are half of the allostatic loading measure, with the other half being stress-related hormone levels. The Gottfredson paper linked above shows that IQ correlates with physical fitness, preference for low-fat low-sugar diets, and (negatively with) obesity; it also predicts psychological resilience in high stress environments. So everything in the allostatic loading measure is dependent on g.
The current study finds kids with high childhood allostatic loadings have poorer working memories as adults, but both could be driven primarily by differences in parental IQ. If parental IQ has a stronger effect on kids' allostatic loadings than does parental income, but both are correlated with IQ, then we'd expect allostatic loadings to explain more than income. That's how omitted variable bias works: whatever's most closely related to the omitted variable picks up the variance that ought to be attributed to the missing variable.
I'm sure the actual causal mechanism is pretty complicated. Low parental IQ will simultaneously provide kids with genes predisposing them to low IQ and with environments to which they're least likely to show resilience. Leaving parental IQ out of the mix doesn't seem a great start to an answer though. Without it, there's no way of disentangling the separate and (likely) augmentative effects of genetically-transmitted IQ and low status/higher stress childhood environments.