The complementary Morita-class count conjecture for blocks of symmetric groups at p=2 and p=3

Let $p$ be a prime, let $w$ be the weight of a $p$-block of a symmetric group, and let $M(p,w)$ denote the number of Morita equivalence classes of $p$-blocks with weight $w$.

Complementary Morita-class count conjecture.

$$M(p,w)=\begin{cases} 2&\text{if } p=2,\ w=3,\\ w&\text{if } p=2,\ w>3,\\ \left\lfloor\dfrac{3w^2+2w}{4}\right\rfloor&\text{if } p=3,\ w>0. \end{cases}$$

The statement is presented as a complementary pattern for small primes, in a setting where much less is known for weights $w>3$. Its general validity is not established in the source and remains open.