Weight training has developed all types of stereotypes with triathletes. Many believe that weight training will bulk them up. Thus slowing them down by adding extra weight. This goes along with the stereotype that athletes such as body builders and explosive sport athletes are the only athletes that need or do weight training.
Here is what research says
1) Running economy (RE) is how efficient one is at using oxygen while running. Several studies have claimed that rate RE can be improved through weight training. One study did weight training specifically with triathletes and found that RE as well as leg strength and power was increased.
2) Plyometrics and explosive weight training may be useful for improvements in endurance athletes. Examples of plyometrics would be one foot hops, bounding and skipping to name a few. Explosive weight training would include hang cleans and push press type lifts.
3) Weight training appears to be most effective in using periodization. The weight training should match the periodization phase of the other training leading into the peak race.
It appears that strength training has some useful benefits yes even for a triathlete.
As for bulking up? It is illegally you will bulk up that much as when one dose lots of cardio work the body naturally slims out.
The human body is smart. It realizes that you are using more slow twitch muscles when doing endurance activities such as triathlon. As a result your fast twitch muscles shrink in size as fast twitch are not being used as much. This is useful in becoming more efficient as fast twitch muscles will take up more energy and oxygen than slow twitch mussels. When the fast twitch muscles shrink they use less energy. Thus your body is adapting to becoming more efficient in endurance activities.
In all the benefits of weight training for a triathletes are many. As one can improve RE, power and leg strength. These elements put together potentially will equate to a stronger and faster triathlete.