What research backs up that too much dairy causes constipation?

Answer

Here are some articles that might be of interest outlining the concerns between milk and constipation:
Does Milk Cause Constipation? A Crossover Dietary Trial
Intolerance of cow’s milk and chronic constipation in children

However, this review of the literature shows limited evidence between cow’s milk and constipation.

And not all dairy is the same. A recent review of 11 clinical trials suggests that short-term (10-28 days) probiotic supplementation (e.g. yogurt with live cultures, kefir, sauerkraut, miso soup, tempeh) can decrease intestinal transit time, with greater effects in constipated or older adults and with certain probiotic strains.