I just started weight training 2xs a week (45min sessions). I already have definition in my legs (I'm a runner) and my arms (I have a clingy 20 month old) but when can I start to see some changes in my mid section and start to see inches decrease?

My goals are to lose another 10-20lbs, fit into a 6/8 and lose about 10% on my body fat (I think I'm around 37% now, using measurements and an online calculator). I plan to do this my continuing to incorporate weight training 2xs a week, run 4xs a week and stick to calorie counting.

You should be able to see changes of some kind within a month, but the changes that happen depend on the particulars of your body and how you are training. You will lose inches, probably, but it may not be quickly--though possibly half an inch to an inch within a month around your natural waist. You will definitely see further definition in your arms and legs. You are very unlikely to lose your belly completely and see visible "abs" until you get down to a pretty low bodyfat percentage--in the range of under 21%, I'd say, or perhaps even lower.

Oh no, I'm not expecting visible "abs" too much loose skin for that. I'm most interested in firming and losing inches/weight.

You'll see and feel changes all over your body, including your midsection, by 3 to 6 weeks of training--assuming you are actually challenging your muscles with the training, and attending to post-workout nutrition.