Grass clippings have a Carbon to Nitrogen ratio of around 12:1 which means they can be digested pretty fast which means the bacteria digesting them can generate a lot of heat which can "cook" those "weed" seeds. Many years ago when I still believed that grass clippings needed to be picked up I noticed that they would start producing heat very quickly, often while still in the catcher bag on the mower.
Just be careful where you pile up those grass clippings since they can generate enough heat to spontaneously combust, and the gases generated as they are digested will displace the oxygen you need in enclosed places. People have died from asphyxiation where grass clippings have been piled up in enclosed spaces.

So since I don't have enough browns to compost them, do you have any other ideas on how to use them?

Try searching for some free or very cheap browns in your local area. I get free shredded wood mulch from my city. Others have said that tree services frequently have it for the taking. How about shredded paper from an office, or cardboard?

My grass clippings, when I bagged them, would get hot enough to kill any weed seeds without adding any brown material. If not careful when using grass clippings back then as a mulch I could burn the plants where the grass clippings were used.
Why do you think you need to add some browns to those grass clippings?

Shredded paper, toilet paper rolls, dryer lint, cereal boxes, cardboard egg cartons, dryer lint, sticks. There are a lot of sources for browns if you take a look around. I've used wood pieces in a pinch as well. They won't break down as fast as the grass but you can pull them out and add them to the next batch.

Kimmsr, I want to thank you for your advice. I have almost the same situation, 3/4 grass clippings, 1/4 almost finished (still hot) compost with a lot of maple seeds I'd like to recook. Came here to find out if I needed more browns and read your thoughts on the subject, combining them should give me plenty of heat to cook those seeds. I appreciate the time you took to post.

I am using the grass clippings this year to recover areas of my property. Putting down a layer of cardboard box and then piling on the clippings. Hoping to be able to plant a 30 x 10 foot section of flower garden next year.

I tried this last year with newspaper and tilled them into the soil and planted grass seed in a area this year and it worked well. The old area was a tree stump that had been rotted.