Unlike video coding for professional content, the delivery pipeline of User Generated Content (UGC) involves transcoding where unpristine reference content needs to be compressed repeatedly. In this work, we observe that existing full-/no-reference quality metrics fail to accurately predict the perceptual quality difference between transcoded UGC content and the corresponding unpristine references. Therefore, they are unsuited for guiding the rate-distortion optimisation process in the transcoding process. In this context, we propose a bespoke full-reference deep video quality metric for UGC transcoding. The proposed method features a transcoding-specific weakly supervised training strategy employing a quality ranking-based Siamese structure. The proposed method is evaluated on the YouTube-UGC VP9 subset and the LIVE-Wild database, demonstrating state-of-the-art performance compared to existing VQA methods.