34 is prime time!
Actually, it's 5 years past the age where hitters typically begin a modest decline, and a year past the age where most players begin to decline at a sharper rate.
On the other hand, some players do age very well, and a few even become better players in their 30's than they were in their 20's. When he came to the Twins in 1991, Chili Davis was a poor defensive outfielder who didn't hit for a high average, but he could draw walks and hit for power. At age 30, after 9 season, Chili had managed an OPS+ season over 140 just once, and none in the 6 years prior to coming here.
Yet starting at age 31, Davis would post OPS+'s over 140 three times, and two more seasons of at least 130 before retiring at age 39. Even his final season's OPS of 108 was in line with the production he had managed in his late 20's.
Chili isn't a great comp for Willi, but he's not bad one, either. If JW ages well and posts a pair of OPS+'s in the 120's to go with the 140 he put up in 2012 and play tolerable defense in a corner OF spot, the Twins will have gotten a bargain. And that should be true whether they keep him or move him for the worthwhile sort of prospect that kind of bargain player should bring in trade.