I am a Philippine citizen and I recently visited the UK for 2 1/2 weeks and I would like to go back while my visa is still valid. I would like to stay longer, maybe more than a month, and I would still be staying at my girlfriend's house which I stated on my visa application form from my previous visit. Do I need to show further proof during my next visit or can I just come and go within the 6 month validity of my visa which does say multiple entry?
Do I need to show further proof during my next visit
If you put that question to a high street solicitor who has a practice area in visitor visas, they would strongly advise you to carry all of the evidence you used to obtain your entry clearance. This has always been part of advice and it applies to you based on what you wrote.
I just come and go within the 6 month validity of my visa which does say multiple entry?
Yes, multiple entry means you can visit several times during the validity of your visa. You can expect a landing interview conducted by the Immigration Officer just like everyone else. The interview becomes more probing on successive visits, but your entry clearance supported by evidence should prevail (all other things being equal, i.e., the premise of your visit is the same).
If the premise of your visit has changed, you should tell the IO and expect to be asked for additional evidence. The law requires IO's to be reasonable and if you can produce satisfactory evidence for a repeat visit, there will be no problems.
It is also part of standard advice that personal impact and articulation skills are the sole determinate for whether or not you are successfully "landed".
Finally, your girlfriend should be in the arrivals area and ready to assist the IO should the need arise.