The weather in DC at this time of year can be a bit of a mixed bag. It's very much a transition period as we head into the humid, hot summer. We can get anything from picture-postcard spring days to rainy and overcast with low clouds and mist. Snow is even possible, but it's rare by the time the cherry blossoms come out.
Clear and Sunny
Spring in DC often brings glorious sunny spring days with sparkling clear air without any of the thick humidity haze we get in the late-summer.
If you're lucky enough to be at the Tidal Basin for one of these clear days, you'll find that the clear blue sky naturally contrasts in a very pleasing way with the white or pink flowers. Using a polarizing filter will make that contrast even more dramatic by reducing glare both from the sky (making it a deeper blue) and from the flowers (bringing out some of the detail).
Drizzle and Rain
It's also common to have a few days in a row of cool, drizzly weather. In fact, not having bright sunshine can be a blessing. The cherry trees lend themselves to misty, atmospheric shots. And the softer light can often make the cherry blossom flowers look even more beautiful, since you don't have the contrast problems that come with direct sunlight.
Even in the rain, there are all sorts of photographic opportunities with the cherry blossoms. If it's a misty kind of rain, try getting in close to a branch of flowers in the foreground and get the far shore through the mists in the background. Or, if there are drops of water on the flowers, get in as close as your lens will focus to capture that. And since the walkway around the Tidal Basin is old and not perfectly even, there are often puddles that can reflect the flowers above.