Investing up front is mathematically the best way to invest. That being said, sometimes it will not work out well, for example if you invest your yearly $5500 in your IRA then two days later the market crashes 40%. If that's not something you can handle, DCA weekly or monthly is the way to go. Over the long run there will be more times that it raises than it crashes, but the crashes will happen.
One thing to keep in mind is that most investments are DCA when you look at a long time frame. Even if you invest $5500 on January 1st every year, you're still DCA over a 20 year time frame. Some years your investment will go up during the year, some it will go down and you'll wish you'd waited. Over the long run there'll probably be more where it goes up. The same with yearly bonuses, tax return, etc etc. The only things that aren't DCA in some way are one time life events, like inheritances or maybe a real estate sale. Personally if I got a large inheritance or won the lottery, I'd probably DCA over a year or two as a bit of downside protection.
As far as whether DCA weekly or monthly is better, I don't think it matters very much. Just do whichever is more convenient for you. Generally going along with your pay rate will be the most convenient.