Let $mathcal S$ be a second order smoothness in the $mathbb{R}^n$ setting. We can assume without loss of generality that the dimension $n$ has been adjusted as necessary so as to insure that $mathcal S$ is also non-degenerate. We describe how $mathcal S$ must fit into one of three mutually exclusive cases, and in each of these cases we characterize by a simple intrinsic condition the second order smoothnesses $mathcal S$ whose canonical Sobolev projection $P_{mathcal{S}}$ is of weak type $(1,1)$ in the $mathbb{R}^n$ setting. In particular, we show that if $mathcal S$ is reducible, $P_{mathcal{S}}$ is automatically of weak type $(1,1)$. We also obtain the analogous results for the $mathbb{T}^n$ setting.We conclude by showing that the canonical Sobolev projection of every $2$-dimensional smoothness, regardless of order, is of weak type $(1,1)$ in the $mathbb{R}^2$ and $mathbb{T}^2$ settings. The methods employed include known regularization, restriction, and extension theorems for weak type $(1,1)$ multipliers, in conjunction with combinatorics, asymptotics, and real variable methods developed below. One phase of our real variable methods shows that for a certain class of functions $fin L^{infty}(mathbb R)$, the function $(x_1,x_2)mapsto f(x_1x_2)$ is not a weak type $(1,1)$ multiplier for $L^({mathbb R}^2)$.