So I did my 3rd batch ever making a Dogfish Head 60 min IPA clone steeping grains and using DME:
Ingredients
US measurements (metric measurements)
8 lbs 8 oz of DME (3.85 kg of DME)
1 lb of crystal 40L (0.45 kg of crystal 40L)
1 oz Warrior hops(substituted Columbus)(28.3 g of Columbus hops)
1.75 oz Amarillo Gold (0.75 oz brewing and 1.0 oz dryhop) (50 g of Amarillo hops (21.3 g brewing and 28.3 g dryhop))
1.25 oz Simcoe (0.75 brewing oz and 0.5 oz dryhop) (36 g of Simcoe hops (21.3 g brewing and 14.2 g dryhop))
WYeast American Ale 1056 - 125ml activator
Made a 2 liter yeast starter.
Ended up overshooting the original gravity by quite a bit: 1.082 instead of around 1.070. (Yes, I should have diluted it for more beer

)
After two weeks I dryhopped by just dumping the hops into the primary.
OG 1.082 to FG 1.020 (about 8.25% ABV I think)
A week after dryhopping I bottled. I used 4 grams (113 oz) corn sugar, ending up with about 16 liters of beer to bottle (4.23 gallons).
I used Abbey de Leffe bottles with standard bottle caps and a typical double lever bottle capper. They all seem properly sealed.
Stored the beer around 68 F for three weeks. There's even some sediment in the bottles.
Just tried the beer and it is barely carbonated.

I tried two bottles and both had the same carbonation (or lack thereof).
The yeast should have taken the alcohol content fine. I'm not sure what to check or what happened exactly. The flavor is great, so I don't want to get rid of it (and I'll drink it like this if I have to), but it just needs a lot more carbonation.
I don't need to wait longer do I?
Any idea of what went wrong or what to check or is there anything I could do to get the carbonation going?

Help!