Have you tried hitting the "Edit Scene" button in OBS and then scaling the picture to the desired size?
Also, make sure that in your settings in the "Video" category, you set the right Resolution (for example 1920x1080 for full HD or 1280x720 for HD).
In the game capture settings try checking or unchecking the box for "Stretch Image to screen".
Lastly, what is your internet speed? If the stream is only lagging for you, then I suspect your bandwith is used up.