I do weight training as well, but I must admit that I do my training in periods, with more weight training in the autumn and winter and less in the spring and summer. I do all sorts of training, skiing, weights, running, swimming, cycling and triathlon and I enjoy mountaineering, so in order to manage them all I focus on different training every season. Spring is running, road cycling and telemark skiing, summer is triathlons, running, mountaineering/glaciering, cycling and open water swimming, autumn is mountain biking, running, some mountaineering and weights, winter is running, skiing (classic, skating, touring and back country) and spinning.
I have both tried a split like the one you mention, but right now I follow a full body workout. For me the most important part for progress is to be systematic and actually follow it up. The most striking effect of weights is that I tend to have fewer running injuries when I'm quite strong.