The answer to your dilemma comes from looking at the entire game, not just laning phase. Building a Warwick as a tank will be a pain to deal with in lane. However, as a tank, he lacks the tools of many tier one tanks such as Nautilus, Malphite, Cho'gath, Galio or Alistar. Sure, he can be a pain in lane, but so will Soraka, Karma, and others. If you can survive your lane with similar farm, then most other champions should bring more to the team fights in lane game.
First, don't trade with him. Between his Q and his passive autoattacks, WW has one of the highest levels of sustain in the game. Recognize this and avoid getting baited into exchanges that provide him a lane advantage.
Second, play people who provide better team support but still have sustain. Cho'gath and Vladimir top lane both fit this bill. Cho'gath's passive heal from creep kills can easily keep him in lane. Plus Chogath's silence prevents WW from running up and Q'ing the WW. Vladimir brings more damage and can sustain in lane almost as well as WW. Even better, both of these champions clear waves quickly. Since WW can't, you can push him into his tower and force him to compete with the tower for last hits.
You also mentioned mid lane. While he doesn't have sustain, Galio naturally gravitates towards magic resistance items which significantly decreases WW damage. Plus Galio can wave clear as well, forcing WW to have to last hit against his tower. Otherwise, focus on AP's who clear waves quickly at range, negating WW's ability to run up Q, and run back. Cassiopeia, Anivia, Ahri, and Morgana all can deal with WW middle.
I haven't seen anyone play WW as a competitive AD. Take a Soraka, heal your AD, and let the AD farm away. As a ranged versus a melee, any of the standard bot AD's should be able to harass WW out of lane. Plus, a farmed AD is significantly more important late game than a farmed WW.