Decreasing size of video

As LluisV suggests, you need to expand the export window to reveal the scroll bar to be able to scroll down into the video tab to change 'Bitrate Settings'. Leave Bitrate Encoding as 'VBR, 1 pass' but change the 'Target Bitrate' setting.

You currently are on 10Mbps and if that is getting you a 3.7GB exported file then reducing the setting to (say) 5Mbps would give you an approx 1.85GB file (half the file size). Though reducing the target bitrate is a trade-off between file size and quality. The smaller the bitrate (and file size) the lower the picture quality. Depending on how visually complex your video is - busy images/fast motion (complex) or perhaps talking heads and simple graphics (not complex) will also affect how the exported video looks. You may need to experiment with a few bitrates and have a look at the exports and see if they are acceptable at lower bitrates.

Also keep in mind that if you plan to upload you video to YouTube or Vimeo etc, these platforms will re-encode your video and may add additional quality loss. A minimum of 10Mbps bitrate (and preferably higher - 16Mbps) will give you better results on YouTube.

That said some videos for a client we encode at 1280x720 (frame size) and 3Mbps to achieve the lowest possible file size and OK/acceptable quality.

Make the export window bigger and go to the end of video tab.

With this video reports I use 1920x1080 9Mbps or 1280x720 3Mbps.

Hope this helps.