* Corn hits one-week low after 5-1/2 month high on Monday

* Soybeans steady, consolidating below Monday's 2-year top

* Grain markets weighing Midwest dry weather, Chinese demand

CHICAGO, Sept 1 (Reuters) - U.S. corn and soybean futures consolidated on Tuesday after recent rallies, as questions lingered about the size of upcoming harvests.

Wheat futures leapt higher at the Chicago Board of Trade, supported by firm prices in the Black Sea region and concerns about tightening supplies in exporting countries, brokers said.

Dryness in the U.S. Midwest grain belt, along with the impact of a mid-August windstorm in Iowa, have led traders and analysts to scale back previous projections for massive autumn corn and soybean harvests.

Uncertainty about the size of the harvests should continue to underpin prices for both crops, said Jim Gerlach, president of Indiana-based A/C Trading.

"Until you define what this crop size is, you're going to have a hard time taking it down too far," he said.

The most-active CBOT soybean contract was flat at $9.53-1/2 a bushel by 11:44 a.m. CDT (1644 GMT), easing back from Monday's two-year peak of $9.66-3/4.

CBOT corn was down 1-1/4 cents at $3.56-1/2 a bushel. It earlier touched a one-week low of $3.51 as it eased back from Monday's five-month high of $3.64-1/4.

The USDA, for the second straight day, said private exporters sold 596,000 tonnes of U.S. corn to China for delivery in the 2020/21 marketing year that began on Tuesday.

Analysts expect large global supplies of corn, soybeans and wheat.

However, wheat crops in exporters like Argentina have struggled with unfavorable weather, helping to support CBOT wheat futures, Gerlach said.

"A lot of the major exporters didn't have great wheat crops," he said.

CBOT wheat was up 14 cents at $5.66-1/4 a bushel, after reaching its highest price since April 1 of $5.68-1/2. (Reporting by Tom Polansek in Chicago, Gus Trompiz in Paris and Naveen Thukral in Singapore; Editing by Subhranshu Sahu, David Evans and Richard Chang)