If you want a lightweight program, it is not the compiler you need to worry about so much as the code you write and the libraries you use. Most compilers will produce similar results from the same source code.
For example, using C++ with MFC, a basic windows application used to start off at about 900kB and grow rapidly. Linking with the dynamic MFC dlls would get you down to a few hundred kB. But by dropping MFC totally - using Win32 APIs directly - and using a minimal C runtime it was relatively easy to implement the same thing in an .exe of about 25kB or less (IIRC - it's been a long time since I did this).
So ditch the libraries and get back to proper low level C (or even C++ if you don't use too many "clever" features), and you can easily write very compact applications.
edit
I've just realised I was confused by the question title into talking about lightweight applications as opposed to concentrating on performance, which appears to be the real thrust of the question. If you want performance, then there is no specific need to use C, or move to a painful development environment - just write good, high performance code. Fundamentally this is about using the correct designs and algorithms and then profiling and optimising the resulting code to eliminate bottlenecks and inefficiencies. Note that these days you may achieve a much bugger bang for your buck by switching to a multithreaded approach than just concentrating on raw code optimisation - make sure you utilise the hardware well.