Buy when you have the money, sell when you need the money.
I understand that - my question is more along the lines of: "Does the benefit of dollar-cost averaging over a more frequent period outweigh the potential downside of holding that cash over the span of 2-4 weeks over the course of a year?"
On average, markets go up. That's why we invest in the first place - we expect our investments to go up over time.
Therefore, holding on to investable cash and waiting one, two, or three weeks to buy investments is, on average, a losing proposition. (There are times, like now, where holding on to cash for a short while, may turn out better. But there are also times, like most of the last 10 years, where it would not be. Again, the averages are not in favor.)
Therefore, were I in your shoes, I would invest whatever excess amount above cash flow and emergency fund needs at your earliest convenience every paycheck. Over the length of your career, I think the odds are in your favor.