It could be that you're not exposing your image quite enough. Try a few seconds more to see if that helps.
Also -- try developing in straight white vinegar first for about 30-60 sec, then washing in water. We have alkaline water here & I found that an initial development in vinegar first helps. It also gives a really nice dark blue tone to the print.
Your paper might need a vinegar soak before use as well. A lot of papers use calcium carbonate as a size, and that will affect cyanotypes. Pre-soaking the paper in straight white vinegar untl all the bubbles stop will help. Just be sure to give the paper a good rinse & dry before using.
Good luck with it.