I live in a town house and have neighbors on both sides but we don't have fences in our backyard. I would say that the majority of the lawn is under direct sunlight all day except for a small area that is shaded due to a neighboring tree. In addition, the lawn is a high traffic area which gets walked on every day and kids play on it. Also, the lawn maintenance is done by a landscaping company so I don't have much control over it (other than roping off areas not to be cut yet).
About 6-7 weeks ago I started a project of putting in a stone patio that I got free from kijiji. I ended up getting busy and left everything how it was. I didn't get a chance to level it, fill the sand, and replace the pavers that broke. I did however have time to water twice a week and started to notice more and more weeds taking over.
As you can see in the pictures, the lawn is totally taken over by weeds.



Now what I'm asking is, what's the best course of action I can take here? Should I just tear up the turf and start over? can I lay down grass seed right on top? why do you think the weeds took over so quickly? I do water 2-3 times a week around sunset time. Do you think it could be the lawn mowers the landscaping company is using are introducing weeds from other lawns?

You may be wondering why it looks like somebody dug up part of the yard. There's always been this one area that grass never grew and every time it rained, puddles formed. I always thought these spots are where concrete posts were for an old fence. Yesterday I decided to dig one (then the rest) up and it turned out to be some flagstone. My guess is that there used to be a walkway over here and who ever lived here before dumped dirt over it. The complex dates back to the 1960's so who know's what else could be buried here!

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I'm working with a small space here and need some advice on what I should do.

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