The temp was good - about 68 degrees throughout. And, if you count the brew day as day 0, it bubbled like crazy on day 1, moderately on day 2, slowly on day 3, and then stopped. Everything besides the SG looks good, and when I popped it open for the first time on day, I was almost knocked over by what I think were alcohol fumes. So you think I should just chill for a few weeks and drink? It is already in a keg, but I was going to wait til this weekend to carbonate.
bubbling airlocks are only a moderately accurate way to determine whether fermentation is complete. Since you are mentioning gravity readings I take it you have a hydrometer. I would always measure sufficient samples to assure myself that the gravity hadn't changed for at least 3 successive days before concluding that it was finished. Sometimes when confronted with a fermentation that seems to have stalled out early, people try to "rouse" the yeast by raising the temperature (i.e. move the fermenter to a warmer spot in your house) or by gently (and carefully if we're talking glass carboys) swirling your fermenter to get the yeast back into suspension. Or you could indeed throw in a sachet of an attenuative dry yeast, say S-05 or Windsor or Nottingham
It might help to know what yeast you used, and whether this is a kit using dried malt extract. Some brands of DME aren't as fermentable as expected, leaving you with a higher than expected FG. Or, if you're doing all-grain, high amounts of crystal and caramel malts can lead to a higher than expected FG, don't know how you calculated your anticipated final gravity; maybe you already took that into account.
Some people suggest a week of primary fermentation followed by two weeks of "secondary" or conditioning followed by 3 weeks to carbonate naturally, the "1-2-3" method. For most English styles, like brown ale, depending on the yeast, I usually find that a 5 day primary followed by 10-14 in a secondary vessel, i.e. off the original yeast lees, is enough, and instead of the three weeks of natural carbonation i often merely force carbonate over a period of 2-3 days. Since you say you have it in a keg I assume you a) already racked it off the yeast;
have force carbonation capacity...and, I guess, c) have decided not to bottle it? You could carbonate it and drink it a little green (hard to be patient with your first one) or give it a few more days, to mature, a chacun son gout. Personally I'd let it sit at least 10 days after transfer; even if it's not fermenting violently enough to be visually obvious, the little yeasties are still alive and working, finishing things off, cleaning up and rounding out the flavors.
PS, you still are at 3.999% ABV, a little low but within style guidelines, I think, for a brown. Higher FG may just mean a little too sweet and a little more body than you expected.