Q:

Why does the District of Columbia have its own Court of Appeals?

Geographically, it looks like DC should be part of the Fourth Circuit. With such a small population, only about 3% of what the other Circuits have jurisdiction over, why does it get its own?

A:

Because cases challenging actions of almost any Federal agency or department are typically filed at the head office of that agency or department, which is usually in DC. Similarly, national organizations of all kinds who are affected by some government action often file a case from their own national headquarters, which is often in DC. Thus the DC circuit has a much larger volume of cases and appeals than its population would suggest. 
According to the Federal Judicial Caseload Statistics 2018 Tables the numbers of Appeals Court cases by circuit were:

`      Commenced      Terminated      Pending
 `
.       2017   2018     2017   2018     2017   2018

Circuit      
DC     1,184    872    1,190  1,029    1,446   1,289
1st    1,538  1,213    1,488  1,322    1,408   1,299
2nd    4,450  4,316    4,382  3,937    3,252   3,631
3rd    3,477  2,926    3,745  2,969    2,297   2,254
4th    6,136  4,166    6,185  4,506    2,497   2,157
5th    8,270  7,217    8,235  7,359    5,021   4,879
6th    5,164  4,401    5,195  4,900    3,197   2,698
7th    3,332  2,754    3,452  2,652    1,669   1,771
8th    3,571  2,850    3,154  3,040    2,102   1,912
9th   11,504 10,804   12,032 12,030   12,789  11,563
10th   2,275  1,862    2,296  1,848    1,216   1,230
11th   8,050  5,982    7,686  6,240    3,905   3,647
Total 58,951 49,363   59,040 51,832   40,799   38,330`

Similar data is available for other years, and for district court cases. These seem to show that caseloads for the DC or "Federal" circuit are comparable to those of the smaller circuits. This does not take into account any question of complexity levels.
Also, it looks to me as if the percentage of District Court cases which are appealed to the Circuit Court level is higher in the DC circuit than in most of the other circuits.

