SHANGHAI, Nov 28 (Reuters) - Hong Kong stocks fell on Tuesday, while Chinese shares closed slightly higher in a rangebound session amid sluggish recovery in the country's economy and weak investor sentiment.

** Hong Kong's Hang Seng Index ended the session down 1%, and the Hang Seng China Enterprises Index declined 1.1%.

** The blue-chip CSI 300 Index and the Shanghai Composite Index both edged up 0.2%.

** Other Asian stocks nudged higher, while the dollar wallowed near three-month lows as investors remained convinced the Federal Reserve was done with its rate-hike cycle and looked ahead to a crucial inflation report later this week.

** "Recent China economic data is still relatively sluggish and does not resonate with the Fed's slowdown in interest rate hikes," said Li Yanzheng, fund manager at Fortune & Royal Asset.

** "So the market struggles, as the big-cap stocks remained weak while small stocks outperformed."

** Shares on the Beijing Stock Exchange, which focuses on China's small companies, dropped 4.2% after surging 11.4% on Monday amid frenzied bets.

** The bourse vowed to strengthen regulation and maintain a normal trading order on Monday after shares on the index rallied more than 50% since a recent low in October.

** Profits at China's industrial firms extended gains for a third month in October, albeit at a slower pace. Investors are still concerned about the weakening property and related sectors.

** China's central bank said it would fend off systemic risks to the economy and use forceful and targeted monetary policy to better support domestic demand.

** In mainland markets, healthcare shares and automobiles rose 1.8% and 3.6% respectively, leading the gains.

** Hong Kong-listed tech giants dropped 0.8%, with food-delivery giant Meituan down 5.2% ahead of its earnings due later in the day. (Reporting by Shanghai Newsroom; Editing by Rashmi Aich and Varun H K)