You need a dense enough layer of mulch to prevent those weeds from getting access to the sunlight they need to grow. For some "weeds" a 2 or 3 inch layer of mulch will do that while others need more. At this time of year the winter weeds will not be producing seeds, so that should not be of much concern.

@ kimmsr... Not sure how recycled tires got into this discussion? @ OP... Just called the landscape company that supplies the mulch. It is called "Playmat" mulch. There is no dye in it and it is NOT put through a shredder, rather it is put through a chipper. They claim that it provides more cushion when it's not shredded. The mulch is also NOT heat treated. That's good stuff to know, although shredder vs. chipper is just a matter of particle size in the finished product. The ASTM standards for which play mat mulch is certified are in regard to moisture retention and erosion control. Here's a description of play mat mulch that I found: Play mat exceeds all ASTM (American Society for Testing and Materials) requirements and is superior in quality. Our virgin hardwood chips are processed to create mulch that is clean and free from twigs and leaves. Our playground surfacing compacts in layers to give incredible impact resistance, therefore, receiving one of the highest government safety ratings. He suggested to fluff the existing mulch with a rake and put another 4 inches of Playmat on top of it. This seems like an instruction that is in direct opposition to the results you want. Stirring up the mulch will allow more weed seeds to get to the soil. You could probably have a load of wood chips delivered for free via tree trimming service. The last sentence of the description I pasted above mentions compaction as a factor in impact resistance. If the person you called knew that, that should be more reason for them to not give you the "fluffing" instruction because the reason you have the mulched area is that it's under a play structure. I also asked for a herbicide recommendation and he mentioned that a number of his guests use a product called "Crossbow". I need to do some research on this product. Great idea, putting poison in a children's play area definitely warrants research. If you could go into the future and ask your grown children if they would rather have pulled weeds or played in poisoned wood chips, I think you will have done as much research as necessary, though.

If you could go back in time, you should have had it finish graded the first time. Whatever you do to this soil will have to be repeated when the final soil is in. Then you could have started watering it as if you wanted to sprout new grass seed. That daily watering would have sprouted all the weed seeds and then the RoundUp would have given you a perfect bed for new grass. Even if you kill all the weeds in this current level of soil, the new soil will bring in more weed seeds. When you start watering the new grass, the new weeds will sprout and you'll be starting with a weedy lawn. Looking forward if you had the soil delivered today, you could begin watering daily now to sprout the weeds, spot spray the Round Up in a week, and then do your seed.

>>They sell a giant blow torch at the big box stores, but I can't say that's any safer than chemical! Some weeds emit toxic compounds that can enter the air when burned. Not that particulate matter and smoke are all that good for you, either, and the risk of uncontrolled fire on dry grass... Well, make sure to water very well first... If opposed to any chemical addition, solarization with clear plastic is usually best--although it tends to work better in summer than it would now. Water well, tack down the plastic, and watch the weeds fry and the seeds overheat and die. Black plastic won't heat up as well (it absorbs a great deal of heat, but radiates at least half of that away back into the atmosphere), but will shadow out the weeds over the course of a few weeks. Spring seedings don't tend to go well, but the line of "Too Late" on fall seeding is moving southward. In most locations, you won't have sufficient time, post solarization, to re-establish grass. Depending on your locale and grass type you want to use, dormant seeding might be a better option for you. Let us know.