As far as I know, Google weblight is the faster version of SERP for users in slow mobile internet connections. If your target audience is from a country ( where internet is still a bit slow, like some Asian country ) or using a slow connection to browse the internet, they'll come from weblight. It is simple and there's nothing to worry, you better optimize your site for more speed.
This seems to happen when Google believes your site will be too slow for a particular visitors. If you're seeing this a lot, then it's likely Google thinks you have speed problems, which should look into.
A small amount of these hits seem impossible to prevent, even with relatively quick sites if Google thinks a particular visitor's connection isn't capable of loading your site efficiently.
One related issue is the cost of mobile broadband in some places, where there is a tangible cost of loading heavy sites.
Where are you located and what kind of device is being used to access the site? The only way I know to defeat this is to ask your users to try Bing or any other search engine instead of g (not like that will happen!)
This is a case of "we know better and you, webmaster, should be happy any of your site shows up over such a slow connection."Among items removed are advertisements, images, unnecessary code, usually js but other forms as well.
If you are targeting a geo location which does not have ordinary wifi as a STANDARD you might want to rethink your site overhead and any imaging needed (dump color and go to black and white line drawings).
g presents this as a service to the USER, not the webmaster.