My advice would be to just let it go and not put in any more time and money. Spring seeding is not recommended exactly for this reason, along with the inability of the new grass to make it through the summer heat. Cool season grasses should be seeded in the fall when weed pressure is lower and temps are cooler. They also get a chance to develop a root system before next summer hits.

So the best course of action would be to just mow the weeds and prepare to do a proper renovation mid-August/early-September.

Information on lawn renovation:

http://lawniac.com/lawn-renovation

In the meanwhile you could have a soil test done somewhere locally, it will help identify nutrient deficiencies and other characteristics of your soil.

Agree. The very best time of the year to seed a northern lawn is in the early fall. Every day after that is worse than the previous day. Once you get past late winter, the results are MUCH less satisfactory headed into spring, late spring, and summer. The later it is seeded the faster it dies out and the faster the crabgrass takes over. At this point all you can do is sit it out. You can practice good lawn care management for the next couple of months and plan to renovate it in late August. Here's what to do until then.

Watering: Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 1 inch all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, sprinkler and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps in the 90s, deep water once per week. With temps in the 80s, deep water once every 2 weeks. With temps in the 70s, deep water once every 3 weeks. With temps below 70, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. This deep and infrequent schedule works in Phoenix and in Vermont, so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.

Mulch mow at the mower's highest setting.

Fertilize now with an organic fertilizer like soybean meal, alfalfa pellets, corn meal, corn gluten meal at a rate of 15 pounds per 1,000 square feet. Don't use any chemical fertilizers, herbicides, or insecticides until later. By allowing the weeds to grow you will be developing the soil and putting roots down into it. These roots are important for your soil to develop the right structure.

Then in August do this: Change your watering practices to every day, 3x per day, for 5-15 minutes each time. Do that to sprout all the weed seeds in the soil. After a week of daily watering, spray everything with Round Up to kill all the living stuff. Continue with the daily watering for another week and spray again with RoundUp. This process should clear everything out. Rake up all the dead stuff and you can seed right onto the top of that soil. Roll the seed down or walk on every square inch of it. Then continue watering daily 3x as before to germinate your new grass seed. This approach will give you a pure stand of grass almost guaranteed. When you get 80% germination on your grass seed, start to back off on the watering frequency. Mow when the grass is tall enough to mow at 5 inches or so. At that point look to see if the grass is uniformly dense across the yard. You still will have time to add more seed in the thin areas.