I have a video that I optimized from 150 MB to 30 MB. The video files are hosted on Amazon S3 instead of my website's server.
Will this affect my page speed/SEO since the file is so big?
The file size of an image affects SEO, but not the file size of a video.
Google uses Googlebot-video to check out videos and answer video searches.
In terms of SEO, what will increase your page rank is to have a transcript of your video on your page¹. This is because that way you are going to have good content (hopefully, it's a good video) on your page. Of course, movie like videos should probably not have the transcript...
There is nothing about a limit in terms of file size. The main problem is on you as the amount of Mb is going to increase your bandwidth and thus your costs. Google should not download it more than once, though (maybe once a year)...
That bot was created around 2010. If your video is unique enough, it's going to be found as a video when someone does a video search.
Contrary to what Simon says in a comment, it doesn't need to be using HTML5 tag (although it is probably better to do so!). There were videos before HTML5 and Googlebot-video existed before. i.e. HTML5 was official in 2014 only, the Googlebot-video started working in 2010. So it certainly support Flash videos too. There is a page about videos and indexing on Google (and there is also a video too.)
¹ The Whiteboard Friday vlog by moz are a good example of such transcripts helping moz tremendously in getting high ranked pages.