The two-time victor of the £1 million contest has been given a mark of 170 for the marathon on April 4, 2lb lower than what he was rated after his heroics at the end of last season.
Tiger Roll will have to carry top weight if he is to become the first horse to win the Grand National three years in a row.
Red Rum won three times, but three years separated his second and third triumphs.
Tiger Roll, who a year ago became the first back-to-back winner of the National since legendary triple victor Red Rum in the 1970s, is owned by Gigginstown House Stud - led by airline boss Michael O'Leary and his brother Eddie. He is the 13/2 favorite with Betway, official betting partner of Randox Health Grand National.
However, O'Leary has repeatedly stated Tiger Roll would only bid for another National win if connections were satisfied with his rating, and the immediate reaction to his mark of 170 and the compression of the handicap was one of frustration.
Tiger Roll is the joint-top weight with Delta Force, also trained by Irishman Gordon Elliott, for the race on April 4 at Aintree Racecourse.More news: Damian Lillard to miss All-Star weekend, hopes Devin Booker gets his spot
Ten horses have been given 11st or more and Greenwood said: "This year, 73% of the horses entered are in the handicap".
Fellow Irish handler Willie Mullins, profitable with Hedgehunter in 2005, has spectacular Irish Grand National victor Burrows Saint (10st 10lb) amongst his 9 contenders.
We are 4lbs worse off with Magic of Light [2¾ lengths behind in second last year]. The different mares engaged are Shattered Love (Gordon Elliott IRE, 10st 6lb), Atalanta Ablaze (Henry Daly, 9st 13lb), Cabaret Queen (Willie Mullins IRE, 9st 13lb). His rating of 148 is the same as he carried in 2017.
Other names to highlight are Kimberlite Candy (Tom Lacey, 10st 4lb), victor of the G3 Classic Handicap Chase in Warwick, and the victor of Listed Sky Bet Chase Ok Corral (Nicky Henderson, 10st 9lb).
Predictably, Eddie O'Leary, Michael's brother and racing manager, who was not present in St George's Hall, a magnificent building in Liverpool, for Tuesday's unveiling of the weights, described it as "unfair" and said that they were "disappointed".
"This decision was essentially taken in two factors: the historical compression that was introduced by Phil Smith and has been used for the last 10 years or so".More news: Major League Baseball announces rules changes for 2020 season
"Tiger Roll is a brilliant, brilliant horse and he is completely invaluable to us, but we have to do our best by the horse".
"Tiger Roll was rated 172 at the end of a year ago and obviously there is no recent evidence to continue due to its fitness problems, so its disability mark has not been quantifiable since then".
"He is therefore coming down 2lb and carries the same weight as Suny Bay did when he was second in the 1998 Grand National".
The best weight-carrying performance of recent years came in 2015 when Many Clouds, one of the most popular horses, of the past decade, shouldered 11st 9lb.
"It must be remembered that Tiger Roll ran in the race off a rating of 159 but was actually rated 167 at the time due to his win in the Cross Country at Cheltenham".
"Tiger Roll has also not yet qualified for this year's National".More news: Celtics Ranked 5th Most Valuable Franchise in National Basketball Association
The O'Learys have suggested he might not run at Aintree if the handicapper is considered to have treated their horse unfairly, although many believe they will not easily turn down a chance at making racing history.