바라보다 is looking at something steadily from a little distance, which makes it the verb both for gazing and for taking a view of something. -게 supplies the attitude: 날 이렇게 따뜻하게 바라보는 남자 'a man who looks at me this warmly', 멍하게 바라보게 되더라구요 'I found myself staring blankly at it'. Figuratively: 지금보다 100배는 더 안 좋게 바라봤습니다 'people saw it a hundred times more negatively', 이전의 나를 너그럽게 바라봐 줄 수 있는 'being able to look kindly on your former self'.