I like this phrase quite a lot as I always picture a watermelon rolling and then falling on its heaviest side. It’s used as a metaphor to say that people generally tend to side with those who will benefit them (as opposed to choosing through justice or impartiality), it can also suggest populism or going with the crowd. Below I’ve compiled two super short clips of Wu Nien-zhen’s Human Condition (《人間條件》）in which this phrase is mentioned. I don’t own the copyright to the video and am using the clips for purely educational purposes. Here the woman speaking uses a variation of the phrase: 吃西瓜倚大傍 ﹣ although the 倚 is commonly rendered phonetically as 挖 – which sounds closer to the Taiwanese pronunciation of 倚, which is pronounced “yǐ” in Mandarin. The 旁 is also commonly written as 邊, because it’s closer to the meaning of the phrase in Mandarin. In both cases the whole phrase is used as an adjective.
Again, be careful how you use this phrase, as careless use can offend strangers.
I’ve updated the google doc, for those interested