My old spray head literally fell apart. I replaced with a new head (Danco brand). The problem is that now I get a weak spray with most of the water coming out of the faucet and not the sprayer head.

I am answering my own question. After viewing other entries, I removed the sprayer head and turn on the faucet. I got a good stream so the diverter was apparently okay, and therefore the answer must be in the sprayer head itself. There were two washers in the new head, both either hard plastic or rubber. On a whim I replaced them with the washers from the old head, both a softer rubber. The sprayer worked fine at that point.

I'm glad you got your sprayer operating. For your information the sprayer hose is pressured up every time you turn on the faucet. This puts pressure to the sprayer head but not through it until the trigger's pressed. When you press the trigger it snaps the diverter so it shuts off the spout and opens up the spray head so water sprays out. When you release the trigger the spray shuts off and the diverter snaps open again so the water can enter the spout. Regards, Tom