Cycling jerseys are not meant to be loose. Some, though, are looser than others, as noted above. Terry has some relaxed cut jerseys you might want to look at, along with mountain bike jerseys.
I bought some really cute plain v neck wicking t shirts from Terry a few years ago. I don't wear them cycling anymore, but they are great for other sports. If you find some wicking shirts you like, they will last for years and serve many purposes.
And, although it may seem counter intuitive, loose, flapping shirts actually are less flattering than fitted ones, no matter what your size. You should not be continually worrying about what you look like to others; cyclists wear cycling clothes (jerseys and lycra shorts) and if you are riding, you are a cyclist.