If you want an adjective, weepyweepy (mentioned in a comment) works great for this.
If you want something more descriptive, you can say I cry easilyI cry easily. This works really well in real-world contexts,contexts; for example, someone has just told you a story about overcoming personal adversity, and is surprisessurprised to see you crying. While dabbing at your eyes, you can explain, "I cry easily. What a wonderful story.":
I cry easily. What a wonderful story!