Forgot an important detail that hopefully Don can put into the original post:
Do NOT core aerate after putting down the barrier as when you disurb the soil you are turning over the weed "seed bank" and working against yourself.
I will tell you that most lawns don't even need core aeration but it's a major profit maker for landcapers. Get your organic matter level up and core aeration is completely not needed. Whole nutter' topic.
Grass grows through and around concrete. Do you think soil is harder than concrete? Food (or grass) for thought....
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