Without seeing your story, I can't say exactly what the problem is. And even if I saw the story, I might not think it is "weak." So what I add below will be problems I've seen over time that I imagine would cause someone to classify a story as weak.
1. Characters do not engage the reader's sympathy or grow in important ways during the course of the story.
2. There is no take-away point. The take-away point answers the question, So what? Why would someone care about this story? What is the lesson? The lesson should not necessarily be stated, but it should be clear. (Sometimes in very sophisticated stories, the point may be ambiguous, but there is certainly something that forces a reaction from the reader.)
3. There is no sub-text. Strong stories work on several levels. Besides the main problem, which must be resolved in some way, there are lesser problems that also draw in the reader and demand resolution or at least consideration.
4. The language may be correct, but uninspiring. In this case, weak writing would be missing captivating descriptions and interesting metaphors. Its rhythms may not match the intended tone or message.
Of course there may be other problems that someone would characterize as weak. My best advice would be to ask the person making the comment to elaborate. Dialog around writing is often a writer's best hope for growth.
You may also want to use the sample edit service on this site. Comments are specific and when appropriate, include suggestions for improvement. There is a fee, but it is refunded if the writer goes on to use any of my editing services in the future.
