Small Aircraft; High Wing; 1 Eng; Fixed Gear
Air Traffic Control Fully Certified
Workload
ATC Issue All Types; Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Published Material / Policy
General None Reported / Taken
Human Factors; Procedure; Aircraft
I was working all locals combined and I launched the second aircraft a bit too close.  I ended up having to give the 2nd guy a couple of turns to get 3 miles.  As soon as I had it I shipped them both.  The first guy didn't take the switch and then the 2nd guy sped up a little about 10 knots and the TRACON Controller wasn't able to talk to the first guy and I'm pretty sure we lost the 3.  It was all around a bad call on my part and I should have just waited on the second guy or run him out on a different heading for longer or stopped his climb or anything like that.In my defense; I was working all locals combined which I'm not super proficient with because while we were on COVID schedules.  I will also note the following:1.  I was working LCW combined with other locals which is supposedly not safe per the district because we can't see the runway.2.  No OT used and we are operating with 3 CPCs and an FLM when normal numbers are 8 and an FLM due to quarantine from a COVID positive. 3.  The ATM WILL NOT USE TMI [Traffic Management Initiative] for staffing because of political pressure not because it isn't needed. TMI for staffing have been definitely needed especially this week with 15 ish controllers out of 25 on quarantine.
Tower Controller working 3 Local positions reported an airborne conflict between two departures.