IMO Jump jets are far better for heavies and assaults than for light mechs (meds are mid ground), because very fast mechs can compensate hard terrain in part just by superior movement speed. And even if they weight less for them JJs still cost a big percentage of your total available plus you won't have the ability to cool down big jumps properly because (again) lack of available weight.
Assault JJs weight more but you still can afford it and you also can much more easily afford the extra heat they generate. Assaults will be crippled by slow/impassable terrain, JJs allow them to circumvent that plus you can change your facing at no extra cost for optimal firing or taken damage. They're superb for maintaining the desired range, for stablishing or breaking weapon/vision/sensor range, so superb for hit & run, for jump + alpha -> alpha, for jump + alpha -> alpha + jump (Ace Pilot hit & run), for alpha + jump -> alpha + jump (Ace Pilot jumpy LRM boat, untouchable). They're excellent for offensive purposes, you arrive before where you need to (and with optimal facing), and even better for defense (breaking LoS). You can very easily exploit the AI having JJs in all your heavy/assault non pure LRM boat mechs and cheese most missions. Oh, and as a bonus you get a bit of extra evasion.
With JJs you can cheese many five skull missions with just one assault, and hard but doable with one heavy. That wouldn't be possible without them, at least for me, even if you add some extra firepower. To a large extent they allow you to dictate when and how is the engagement going to happen. And the fact the AI don't have them in all their mechs but you can if you want is a HUGE advantage.