  We consider closed subschemes in the affine grassmannian obtained by
degenerating $e$-fold products of flag varieties, embedded via a tuple of
dominant cocharacters. For $G= \operatorname{GL}_2$, and cocharacters small
relative to the characteristic, we relate the cycles of these degenerations to
the representation theory of $G$. We then show that these degenerations
smoothly model the geometry of (the special fibre of) low weight crystalline
subspaces inside the Emerton--Gee stack classifying $p$-adic representations of
the Galois group of a finite extension of $\mathbb{Q}_p$. As an application we
prove new cases of the Breuil--M\'ezard conjecture in dimension two.
