Recommended key lengths for BLAKE2b
The Analysis of BLAKE2's Modes of Operation paper gives a PRF bound for keyed BLAKE2b with a key of size $k$, under the assumption that the underlying block cipher is ideal (Corollary 3):
$$
\text{Adv}^{\mathrm{PRF}}_{\text{BLAKE2b}}(\mathcal{D}) \le \frac{q^2}{2^{1024}} + \frac{2q^2}{2^{512}} + \frac{q}{2^{256}} + \frac{q}{2^k}\,.
$$
Here, $q$ is the complexity of the distinguisher, i.e., calls to the hash function. 

Given this PRF bound, the MAC security of BLAKE2b with output size $t$ can be derived as
$$
\text{Adv}^{\mathrm{MAC}}_{\text{BLAKE2b}}(\mathcal{D}) \le \frac{q^2}{2^{1024}} + \frac{2q^2}{2^{512}} + \frac{q}{2^{256}} + \frac{q}{2^k} + \frac{q_v}{2^t}\,,
$$
where $q_v$ represents the number of forgery attempts.

Seeing this, two things look clear:


It is pointless to have a key over $256$ bits, since security begins degrading by other means by that point.
The tag size influences the probability that a forgery succeeds; thus, it cannot be small enough that an attacker can succeed 'by chance'.


All in all, the same recommendations for HMAC also apply to keyed BLAKE2. A 256-bit key with a 128-bit tag seems like a reasonable choice for most purposes.