Can the cops prove I was high on weed when I was pulled over and arrested?

I was pulled over for "failure to keep right," and the cop arrested me for being under the influence. It was not a DUI but just under the influence of weed. I refused search of the car at first but it was my fathers and he allowed a search a couple hours later. They found half a joint and some empty bags. I submitted to all tests and passed a breathalyzer for alcohol when I was at the station (. 07). I never admitted to smoking or admitted to anything. He smelt it on me when he pulled me over and said I looked high. My question is, can he prove it in a court of law. I know I will probably be guilty of under 50 grams which was the other charge I received but I would like to know how he could prove I was high.