Idk if the number of stars means anything, tbh.
The Flying Eagle had 5, the White house had 2, the original and the retro have 6, and the current logo has 3
And then shoulders and pants have been inconsistent as well - the third has 4 on the sleeve and 5 on the pants, to (not) match the 6 on the logo
You guys are just over thinking it. It's all a play on three stars, and from there I think they just added stars to sleeves and pants to make it work. They added and subtracted stars from the arms arbitrarily in the 80's, again I think it was purely aesthetic. It all circles back to the use of three stars. Hence three blue, three white. Currently three white on the logo, three white on the Winter Classic from 2015, and three on the Stadium Series.
The three star motif is a reference to the DC flag which is lifted directly off of the Washington coat of arms. Don't believe anyone who tells you mumbo jumbo about it being for DC, Maryland, or VA is wrong. It's lifted from the flag, that's it, there isn't much more to the story. They even took the same star design.