One clarification: thrust-to-weight says something about an engine’s mass (by definition), but specific impulse only says something about the exhaust velocity of the propellant (i.e. the impulse per unit of mass), not the mass of the engine.
So the high Isp is due to the very light exhaust (hydrogen, not water or CO₂) which gives the higher velocity to the gas molecules at a lower temperature?
In a sense, yes. For a given temperature, hydrogen, with 1 atomic mass unit, will have a much higher velocity than water (18 amu, so √18 ≈ 4.2 times as slow) or carbon dioxide (44 amu, so √44 ≈ 6.6 times as slow).
Yes, having lighter exhaust also helps you raise your ISP. Scott Manley has a few videos on this topic, where he explains the science behind this much better than I ever could.
