Do your trimming and joining without recompression in VideoRedo.
It has a free trial.
Vegas always recompresses mp4: note that the recompressed file can be bigger or smaller, depending on bitrate X time.

I do not know how to determine the input bitrate. I am using the default for the output, it appears to be 128 Kbps.

Are you saying that VideoRedo is better than Sony Movie Studio Platinum? I think I tried it but I do not remember why I did not like it.

There is an app you can download off the net called MediaInfo. Is it to open your video and post the Text view results here. The default of which render template.

Are you using MakeMovie or Project > Render As? Using Render As gives you more options.

If you use Make Movie > Save it to my hard drive and do NOT go to Advanced options, MSP 13 uses its own default to render. You can see the data for the file using MediaInfo as MSmart suggests.

You need to go to Advanced options to be able to see the Render As window and choose the template yourself and customize it (including the video bitrate).

MSP 13 (which the OP says he uses) does not have the separate Project > Render As... menu any more. It's all in Make Movie (Advanced options) now.
Actually, in e.g. MSP 11 and 12 Make Movie > Save it to my hard drive gives you the same Render As window as Project > Render As... as well.

Are you saying that VideoRedo is better than Sony Movie Studio Platinum? I think I tried it but I do not remember why I did not like it.

I would say that, if all you're doing is cutting out sections of video, e.g. adverts, Video ReDo is a more suitable tool than SMSP. It is not a true video editor as it cannot add effects to either video or audio but it is very efficient at what it does.

Sony Vegas is an editor and encoder.
VideoRedo is a muxer and stream fix utility.

Completely different tools for completely different tasks; each one is "better" for its intended purpose.

Search.

Yes, MediaInfo helps. The following are portions of the output using the "Sheet" view. So I guess the output bitrate is much greater than the input. So the next step is to know how to set the output bitrate to the same as the input

Input

Format : MPEG-4
Format profile : Base Media
Codec ID : isom
File size : 91.6 MiB
Duration : 11mn 10s
Overall bit rate mode : Variable
Overall bit rate : 1 145 Kbps
Writing application : Lavf56.40.101

Output

Format : MPEG-4
Format profile : Base Media / Version 2
Codec ID : mp42
File size : 351 MiB
Duration : 4mn 4s
Overall bit rate mode : Variable
Overall bit rate : 12.0 Mbps

I have customized the template to use lower bitrates. Bitrates below 1M provide much lower quality. Above 1M is good except there is a flashing affect, I suppose it is a form of pixilation. The output file size however is much greater even when the quality is not as good. So there must be something more than simply the bitrate or how I am changing the bitrate. I am changing the bitrate by keeping everything as the default except choosing a different bitrate in the drop-down.

I get the flashes (pixilation?) even at 13 Mbps.

I used ffmpeg to reduce a file created by Movie Studio Platinum 13 from 51 MB to 9 MB with no loss of quality. See "compression - Reducing video size with same format and reducing frame size - Stack Overflow" at:
http://stackoverflow.com/questions/4490154/reducing-video-size-with-same-format-and-reducing-frame-size

The command I used was:

ffmpeg -i input.mp4 -c:v libx264 -crf 24 -b:v 1M -c:a aac output.mp4

I used that (with crf set to 20, a little less compression) to compress 24 videos and they went from 2.5 GB to 660 MB with no noticeable loss of quality. Small videos tend to be half in size but larger videos compress more, most much more.

So the question is how to do the same as what ffmpeg does using Movie Studio Platinum 13? If that is not possible then the answer to my question is to use ffmpeg separately.

The problem is probably with the "Movies & TV" program in Windows 10. When I play a video that was processed by Movie Studio Platinum 13, even at a low bit rate, using any other video player then there seems to be no problem. So I need to do more analysis but it might be that the solution is as easy as setting the bit rate to a relatively low value.

If you are seeing a 10x increase in bitrate using crf 20, then your input video is very noisy.
It is all the movement and grain that is hogging your bits,.

Just set an average (variable) bitrate of 2,000 Kbps and be done with it.