Despite the commendable progress of recent LLM-based data synthesis methods, they face two limitations in generating table instruction tuning data. First, they can not thoroughly explore the vast input space of table understanding tasks, leading to limited data diversity. Second, they ignore the weaknesses in table understanding ability of the target LLM and blindly pursue the increase of data quantity, resulting in suboptimal data efficiency. In this paper, we introduce a progressive and weakness-guided data synthesis framework tailored for table instruction tuning, named TableDreamer, to mitigate the above issues. Specifically, we first synthesize diverse tables and related instructions as seed data, and then perform an iterative exploration of the input space under the guidance of the newly identified weakness data, which eventually serve as the final training data for fine-tuning the target LLM. Extensive experiments on 10 tabular benchmarks demonstrate the effectiveness of the proposed framework, which boosts the average accuracy of Llama3.1-8B-instruct by 11.62% (49.07% to 60.69%) with 27K GPT-4o synthetic data and outperforms state-of-the-art data synthesis baselines which use more training data. The code and data is available at https://github.com/SpursGoZmy/TableDreamer