There are so many different sizes of Bassets, and from what I have heard, 2 years seems to be the full grown age.
My 3 are on the larger side, but are at their correct weight for their bone size. They are very active, and have great muscle tone. Far from being over weight.
My older two (both around 4 years old) differ in their full weight age.
Dozer was 51 lbs at 10 months, and he hit his current weight of 56 lbs at 18 months.
Digger was also 51 lbs at 10 months, but he was closer to 24 months before hitting his current weight of 63 lbs.
My new addition, Dudley, is just 4 months old and weighs 32 lbs. He's in line with the other two at this age.
I should add that all three are males, intact, and all were the largest in their litters. 12-14 lbs at 8 weeks.
Lightning probably didn't achieve his adult weight until he was about two years old as well. He was always very thin as a puppy and didn't care about eating, but when I got Stomps, when Lightning was about 18 months old, Lightning became obsessed with food and bulked up. Stomps was fully grown when I got him, so I don't know at what age he matured.