Engaging in green investments not only contributes to sustainable development, but its profit potential is also widely recognized. How to reach a balance between financial return and environmental responsibility has become a critical issue. This paper quantifies the relationship between network features and optimal weights by constructing a complex network for stock based on the variance decomposition, while also measures the pollution emission levels of relevant enterprises. They are proxies for economic return and greenness respectively. According to this, a dynamic profitability-greenness balance index is developed, three stock pools with different size are established, and weights are allocated by three types of portfolio optimization models to formulate investment strategies that balance financial return with environmental responsibility. The empirical results reveal three key findings. Firstly, if investors' green preferences change, stocks should be re-screened, requiring two or three portfolio adjustments to transition from green aversion to green preference. Secondly, as the size of the stock pool increases, its overall green level decreases. It’s necessary to sale small amounts of a variety of stocks and purchase large quantities of a few stocks, and vice versa. Thirdly, an increase in the number of stocks in the portfolio leads to a reduction in both the Sharpe ratio and the volatility of returns; however, the investors with a green preference often achieve the excess returns in larger-scale portfolios.