How can I place the weather in the top right corner?

Step 1: Go to Appearance > Customize > Header > Site Title & Taglines.

Step 2: Use the Right Tagline field to add the weather shortcode, like this:

[simple-weather days="2" location="Bucharest, Ro" units="metric"]

To learn more about how you can customize the weather display, you can read the Simple Weather chapter.