New Shepard's launch escape engine produces 310 kN (70,000 lbf for the metrically challenged).
To accelerate away from a rocket booster moving at a max of 3 g, I'll assume the crew capsule should accelerate at a minimum of 3.5 g---the number given by former NASA administrator Jim Bridenstine for SpaceX's Crew Dragon and trunk (with what I believe was a max payload of 6,000 kg, or 13,000 lbm).
If we assume a 3.5 g min for New Shepard's launch escape, then we get a max dry + wet mass of 9,000 kg.
The engine fires for 2 s. If we assume a specific impulse in the ballpark of 250 s, we get a mass flow rate in the ballpark of
$$ \frac{f}{I_\texttt{Sp}g_\texttt{0}} = \frac{310,000 \texttt{N}}{250 \texttt{s} \cdot 9.8 \texttt{m}/\texttt{s}^2} \simeq 125 \texttt{kg}/\texttt{s}, $$
which means a minimum fuel mass of just over 250 kg for launch escape. So we're just under 9,000 kg mass for the New Shepard crew capsule. This happens to be on par with the mass of Crew Dragon without trunk and payload.
And I suppose that if the dimensions are similar, and the materials and structure not too different, then it makes sense that New Shepard's crew capsule would weight about the same as a Crew Dragon.
But I haven't seen any numbers given for New Shepard, and I'm wondering: how off is this estimate? Can someone say more confidently how much the crew capsule would weigh? How much fuel it would carry? How fast it would go during launch escape?