The best lightweight screen capturing software is Camstudio as it is only 11 Mb.
- Record from your screen
- Open source
- Add annotations / audio supported
- Save video in any video format (quality is adjustable/frame rates)
- Screen capturing modes (fullscreen, part)
Also check the OBS Studio and FlashBack Express.
These two softwares got more features than the lightweight Camstudio. You would be able to do a professional job.
- Audio mixer
- Streamlined settings panel for quickly configuring your broadcasts
- Various plugins
- Customizable profiles with customized settings
- Sub region (the screen capturing area is customizable)
But there is this thing that you should note:
- Scene transitions are hard cut. It is not much nice.