* Raw sugar volume more than double the average
* Arabica open interest falls from record high
* Cocoa trade eyes next week's grind data (Rewrites paragraph 1, updates prices; adds broker comment, second byline, NEW YORK dateline)
By Marcy Nicholson and David Brough
NEW YORK/LONDON, April 7 (Reuters) - Raw sugar futures on ICE rallied on Tuesday, turning higher on heavy May/July spreading and concern that nearby supplies may be tightening, while the rallying U.S. dollar pushed arabica coffee futures down from a six-week high.
New York cocoa fell on pressure from the strong U.S. dollar , breaking a four-day streak higher.
The ICE Futures Europe markets reopened after shutting for a four-day long Easter weekend.
Raw sugar futures turned higher on a lack of follow-through selling, traders said.
May raw sugar futures on ICE settled up 0.23 cent, or 1.8 percent, at 12.77 cents a lb. Total volume exceeded 216,000 lots, more than double the 250-day average, preliminary Thomson Reuters data showed.
"There is the perception that there's not much to deliver against the May. The (Brazil) centrals basically were absorbed with their delivery against March," said Michael McDougall, director of commodities for Societe Generale in New York.
"The Thais are too expensive at this point and Brazil is just starting their harvest, so there's not much availability there."
Total raw sugar futures open interest rose by nearly 3,400 lots to 928,109 lots as the market fell from a two-week high on Monday, exchange data showed, surprising traders who perceived this to mean new short positions were added.
May white sugar ended down 60 cents, or 0.2 percent, at $359.60 per tonne.
The strong dollar attracted heavy selling to arabica futures, taking the market below Monday's six-week high, traders said.
May arabica closed down 4.25 cents, or 2.9 percent, at $1.4195 per lb. This took it below a six-week high at $1.4735 reached on Monday, when open interest fell 7,646 lots from the April 2 record high at 207,254 lots, exchange data showed, indicating the rally was due to heavy short-covering.
London May robusta coffee futures finished up $28, or 1.6 percent, at $1,806 per tonne in thin volume.
New York cocoa edged down in heavy volumes, pressured by the dollar.
"Arbitrage activity is quiet. The cocoa market is beginning to turn its attention to European grinds (demand) data expected next week," a London-based broker said.
New York May cocoa futures closed down $15, or 0.5 percent, at $2,785 a tonne, while London May cocoa ended up 3 pounds, or 0.2 percent, at 1,942 pounds per tonne.
North American grind data will be released April 16. (Editing by Ruth Pitchford, Dale Hudson and James Dalgleish)