A giant box you need to carry to the post office, clothes you wear in the snow — both of these things are bulky or large and difficult to deal with.
Inside the word bulky you see the word bulk which refers to the size of something, usually something large. When something is bulky, it has a lot of size or heft, though it is not necessarily heavy. Pillows, for example, are bulky. It's just big in an inconvenient way. Thick yarn, or a sweater made from thick yarn, is also said to be bulky. It's thicker than your average yarn.