Roland GX Micro CUBE
For all of my online video Guitar lessons I am currently using a Roland GX Micro CUBE, which I have found to be one of the best small amps I have ever used.
This tiny Modelling Amp/Combo weighs in at just 6lbs (under half a stone) and is built like a Tank, and incorporates pretty much most of the sounds within it that you would usually have to lay out a ton of extra money for on seperate pedals.
Don't be put off buy it's size, 23cm x 22cm x 17cm, with a 5 inch speaker, as despite this being described as just a 3 Watt amp, this is definately a "Wolf in Sheep's clothing" for sure, and will give you all the power you will need at home for practicing both Clean and Dirty sounds.
These are now a discontinued line, but if you look around there are many second hand one's to be had on the market in various colours, so if you can, search one out and Treat yourself to some real high Quality sound in a very small package.