* HSI -0.6 pct, H-shares -1.1 pct, CSI300 +0.1 pct
* Chinese port firms rise on policy support expected on Wednesday
* HSBC slips after UK fund manager dumps shares
* CNBM leaps helped by Credit Suisse upgrade (Updates to midday)
By Grace Li
HONG KONG, Sept 2 (Reuters) - Hong Kong shares fell to three-week lows on Tuesday weighed down by profit-taking, while the Chinese onshore markets eked out slim gains thanks to outperforming port and liquor stocks.
By midday, the Hang Seng Index was down 0.6 percent at 24,613.83 points. The China Enterprises Index of the top Chinese listings in Hong Kong shed 1.1 percent to its lowest since Aug. 8.
The CSI300 of the leading Shanghai and Shenzhen A-share listings inched up 0.1 percent, while the Shanghai Composite Index rose 0.3 percent at 2,242.24 points. Both swung between negative and positive territory in morning trade.
"Hong Kong has seen some profit-taking above the 25,000-point level," said Steven Leung, sales director at brokerage UOB Kay Hian in Hong Kong. "At the moment we don't see any positive news other than some good earnings... so people are just taking a break before the market moves on."
"The so-called 'Occupy Central' may be serving as an excuse for people to be more cautious," he added.
Activists from a movement called Occupy Central have threatened to lock down Hong Kong's financial district on an unspecified date unless Beijing grants full democracy.
Beijing on Sunday ignored calls by democrats for the right to freely choose Hong Kong's next leader in 2017, leading scores of protesters to take to the streets.
HSBC Holdings PLC was the top drag on the Hang Seng, down 0.8 percent. Star British fund manager Neil Woodford sold his fund's stake in the bank last month, citing concerns about the impact of potential fines from several industry-wide investigations on the group.
Similarly, shares of China Modern Dairy lost 2.1 percent after U.S. private equity firm KKR & Co LP sold its remaining stake in the company.
Port operators, likely to benefit from a policy announcement expected on Wednesday to support the country's shipping industry, posted solid gains.
Shanghai International Port Group climbed 2.2 percent, Yingkou Port Liability soared the daily limit of 10 percent, and Tangshan Port 8.7 percent.
Top index boost Kweichow Moutai gained 2.3 percent, leading gains among Chinese liquor makers.
China National Building Material outperformed among the mostly sagging H-shares, spiking 4.2 percent after Credit Suisse upgraded the stock from "neutral" to "outperform".
Trading in shares of Tianhe Chemicals Group was suspended in Hong Kong following a 5 percent fall after research firm Anonymous Analytics released a report on Monday alleging fraud at the company.
(Editing by Simon Cameron-Moore)