Single weighted means 100% in one foot and 0% in the other, which is good training. Though usually it's about 70%-30% for the forms.
If you look at the way you put force through your front or back leg in moves from the form, it is graduated from the back leg to the front or the other way round, this means that at some point you will be 50-50 in your legs making you unstable. You should how ever move off your back leg to the front leg, but keep your root in your back leg until you are over the half way mark then drop your weight to the front missing out the 50-50 stage.
If you are relaxed and strong enough it will make your martial skills a lot more effective. This is because usually when you tell someone to relax they sink to the floor making it a physical action, but it should be from within. So missing out the 50-50 stage will allow your spirit to rise giving you better mobility and power.
If you practice this a lot then eventually you will be able to keep your position just in front or just behind the 50-50 position. This will have the benefit of hiding and finding your root easier and making you more up right. If you watch masters at a high level practising push hands they usually look like they are just standing there double weighted and move with lightning speed they never commit the body fully to the front or the back.