If they spent two more weeks on their second research expedition than they spent on the first week, they spent 2+3 = <<2+3=5>>5 weeks on the island.
In the two expeditions, they stayed on the island for a total of 5+3 = <<5+3=8>>8 weeks.
On their third expedition, they spent twice as many weeks as they spent on the second week on the island, which is 2*5 = <<2*5=10>>10 weeks.
In all three expeditions, they stayed on the island for 10+8 = <<10+8=18>>18 weeks.
Since a week has seven days, they spent 18*7 = <<18*7=126>>126 days on the island.
#### 126