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Does it use alot of battery? Having it in my notifications screen?

Simple answer: no. Neither widgets nor notifications uses a lot of battery.

However, to be clear, if you're referring to simply having notifications on (for any/all apps), then I'd assume that yes, there is some amount of battery being used to display them (e.g. notification appears on lock screen = probably-super-small amount of battery used).

If you're referring to the Weather and Stocks widgets, then no, I imagine that having them in your Notification Center uses no additional battery.

All in all, I wouldn't worry about it.
 
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