Stuck at 1.02

I have a partial grain ESB that's been in primary for 3 weeks today. I was getting ready to bottle (I do 3 and 3), but the FG is 1.02, supposed to be 1.013 with this kit. OG was 1.05. It tastes awesome already.

Kit called for Wyeast Thames Valley Ale Yeast, which I did pitch, but fermentation didn't start for 2 days. (To be fair, the pack was a year old) so I pitched extra dried cooper's ale yeast after 48h.

Since the taste is good already, I'm going to bottle anyway and RHAHB, but what happened? Was it over-pitched? Did I make a mixed up yeast culture that won't attenuate below 1.02?

Is this extract? If it has been at that FG for multiple checks, then it is finished and should be bottled up. Extract can finish fermenting around 1.020 often for future attempts.

Yep, if it tastes good, just enjoy. What yeast did you use and was it extract or all grain?

You mentioned over pitching and asked if this could be the problem. No. Overpitching is difficult to do, but it can be done. It will not however cause a high finishing gravity. The affects of over pitching are more related to off flavors that can be caused in the beer.

In the future things that can cause a lower than expected finishing gravity.

Under pitching the yeast. Best to go to mrmalty.com and make a starter per the calculators recommendations.

Insufficient oxygen in the wort when the yeast was pitched. yeast need a good oxygen supply up front to reproduce. Carboy should be well shaken for a good minute or two to introduce oxygen. Some people inject oxygen from an air stone.

Poor temperature control during fermentation. Big fluctuations in temperature, or letting the temperature get to low can cause the yeast to stop fermenting early.

If all grain, mashing at too high a temperature can cause a lot of unfermentable sugars to form in the wort. Usually getting into the over 153 deg F range will give you a slightly less fermentable wort. The higher temp, the more unfermentables. Some recipes mash higher to leave more body in the beer on purpose.

Using a lot of specialty malts in the beer. Many specialty malts are designed to leave extra sweetness or body in the finished beer.

Since you used a kit, the last two probably don't apply to your situation.