Webm and mp4 are container formats. Those itself don't have any relevant influence on the file size.
The codec with a set bitrate determines the filesize. For YouTube uploads, follow the current recommendations and you'll see, you should use h264 as video codec.
First, make sure the export has the same resolution and frame rate as the input, unless you intend to change it anyway. If that's fine, my guess is that the bitrate was set too high. The above mentioned recommendations for YouTube show you how high the bitrate needs to be to get excellent quality. However, if your source material is far below that, you should use a bitrate that's closer to its quality.
To calculate a suitable bitrate in advance is difficult, when the codec of the source is different from the codec of the export. It's good to have a higher bitrate than strictly necessary because YouTube will re-encode the video anyway. Chained re-encodings with lossy codecs will reduce quality further and should be generally avoided, but in this case you cannot do anything against that.
WebM uses VP8 or VP9, both need slightly higher bitrates to achieve the same quality as h264. This means as a rough estimate, set your maximum target bitrate to something like 90% of the bitrate of the source material. Make sure it's a variable bitrate, not a constant bitrate, because the variable bitrate is almost always the better choice for quality. Then you should get a file size roughly the same as the source video.
And then there's audio. It makes up a smaller percentage of the filesize. However you should check that your editor is not accidentally using much higher bitrates for audio as the source.