In a quick search, here is what I've found:
Smallest with all the features you want might be the Cobra ACXT645 - although I am basing this guess only on photos and my past experience looking at various models in stores. It appears this product might be discontinued by the manufacturer, although I did find that Best Buy and Home Depot appear to have stock available online.
The Uniden GMR5088 and 5095 also seem to have the NOAA weather channels and an LED light.
Other products that appear to have the weather channels but no LED light: Motorola MU350R, T460, T465, and T480, and the Midland GXT2050VP4 and GXT1000VP4.