Evolution isn't particularly light-weight, HOWEVER imho it's the best email program out there and you should be using it anyway.
Evolution synchronizes your Google Calendar and you can see your next 5 appointments (or at least I currently see 5 appointments there, I don't know whether it only shows a maximum of 5 appointments but also with a time limit past which appointments are ignored) when you click on the date in the upper right corner of you screen.
Notice that Evolution has an option to add Google Calendars which worked when I set up Evolution for Ubuntu 14.04. However, it doesn't work with the version currently in the Ubuntu 14.04 repositories because it can't load the page it tries to load. So probably Google has changed something.
But you still can add your calendars. Add a calendar of the type
CalDAV with these parameters:
URL: https://www.google.com/calendar/dav/[your email address]/events
User: [your email address]
The rest is self-explanatory.