Or did it have a nice vigorous initial fermentation, then followed by 4 weeks of continuing to bubble lightly?
This ^^
This makes me less confident in (but doesn't rule out) my poor yeast health theory. Four weeks is quite a while, but not entirely unreasonable for light bubbling, especially given the potential for some hop creep.
Just to walk you through my thought process, I break this down into the necessary components for getting carbonation:
1) Fermentables
2) Viable yeast
3) Suitable conditions for yeast
4) Time
5) Containment
Looking at each component:
1) You said added sugar at bottling, so the fermentables should be there. Any chance you used the wrong units on your scale? For example, using 5 grams when it was prescribed as 5 oz? Or that you forgot to zero out the container? Or even any chance that you meant to add the sugar, but it somehow got left out?
2) Yeast health remains an open question.
3) It's not a particularly strong beer, so there shouldn't be enough alcohol to cause yeast problems. At 72 degrees, temperatures should have been great for the yeast. Conditions all seem good.
4) The only way three weeks wouldn't be enough is if there was another problem (such as yeast health or conditions) that slowed things down.
5) Others have suggested that you didn't get a good crimp. Since you've successfully done other batches, I'm operating under the assumption that you've got the crimping process figured out. Unless you're using a different type/brand/manufacturer of caps than you've used previously.
My approach* would be to pop one or two of the bottles, add a small amount of yeast, and recap. After a couple of weeks, check both one of the re-yeasted and one of the unaltered bottles. If the re-yeasted bottle is bubbly and the unaltered bottle is not, the problem was yeast and you just need to re-yeast the rest of the batch. If both are bubbly, the problem was time and you're good to go. If neither are bubbly, the problem is sugar or containment; add sugar and yeast to bottle and check again after a couple more weeks, and if that doesn't get you bubbles then it's time to start looking at the caps/capping process.
*Not only
would this be my approach, it has previously been my approach, helping me troubleshoot insufficient carbonation on--and ultimately saving--a batch of delicious dubbel.