  While planets between the size of Uranus and Saturn are absent within the
Solar System, the star K2-24 hosts two such planets, K2-24b and c, with radii
equal to $5.4~R_E$ and $7.5~R_E$, respectively. The two planets have orbital
periods of 20.9 days and 42.4 days, residing only 1% outside the nominal 2:1
mean-motion resonance. In this work, we present results from a coordinated
observing campaign to measure planet masses and eccentricities that combines
radial velocity (RV) measurements from Keck/HIRES and transit-timing
measurements from K2 and Spitzer. K2-24b and c have low, but non-zero,
eccentricities of $e_1 \sim e_2 \sim 0.08$. The low observed eccentricities
provide clues regarding the formation and dynamical evolution of K2-24b and
K2-24c, suggesting that they could be the result of stochastic gravitational
interactions with a turbulent protoplanetary disk, among other mechanisms.
K2-24b and c are $19\pm2~M_E$ and $15\pm2~M_E$, respectively; K2-24c is 20%
less massive than K2-24b, despite being 40% larger. Their large sizes and low
masses imply large envelope fractions, which we estimate at $26^{+3}_{-3}\%$
and $52^{+5}_{-3}\%$. In particular, K2-24c's large envelope presents an
intriguing challenge to the standard model of core nucleated accretion that
predicts the onset of runaway accretion when $f_{env} \approx 50\%$.
