  In this paper we study some properties of Takagi functions and their level
sets. We show that for Takagi functions $T_{a,b}$ with parameters $a,b$ such
that $ab$ is a root of a Littlewood polynomial, there exist large level sets.
As a consequence we show that for some parameters $a,b$, the Assouad dimension
of graphs of $T_{a,b}$ is strictly larger than their upper box dimension. In
particular we can find weak tangents of those graphs with large Hausdorff
dimension, larger than the upper box dimension of the graphs.
