So whatever the gross climb gradient the airplane will perform at that day, the net climb gradient will be reduced by 0.8%.
That's the idea.
From a performance requirement - since the 4.5% gradient is greater than minimum required 2.4%, I can takeoff at a higher weight.
Your use of terminology probably is part of your problem. "Performance" relates to the whole gamut of how the aeroplane does things in respect of accelerations, decelerations, climbs, descents, turns, and so forth.
Talking about gross and net climb gradients is only ONE part of the performance story.
Better to think in terms of .. than minimum required 2.4% under WAT -limiting conditions in the second segment.
So, if you are are at a weight, on the day, which might produce 4.5% gross in the second segment configuration, then you MAY be able to increase weight. Two extreme situations to consider .. and a range in between -
(a) if there are NO obstacles (eg really flat country or overwater, ignoring transient objects), the runway weights were not limiting, and you didn't have other eg ATC restrictions to consider, then you would be able to increase weight until you reached the relevant WAT limit.
(b) if there are obstacles and you are already limited by one or more of those obstacles, then the WAT limit ceases to be relevant and you can't increase weight.
(c) in the more general case, you will be able to increase weight UNTIL one of the various calculation cases becomes limiting. At that point you are stuck with whatever weight you have. Keep in mind, also, that the calculation which is limiting may CHANGE throughout the takeoff.
From an obstacle requirement - I need to ensure the 3.7% clears the obstacles by 35'.
.. for the period you are in the second segment.
I can decrease the net gradient to 1.6% in the second segment if that can clear the obstacles by 35',
.. for the period in the second segment.
which means that I'm also at the minimum performance requirement for WAT limits (25.121)
yes for the first bit. However, as others have observed, treat Parts 25 and 121 as two parts of a whole. WAT limits are part of the aircraft certification and built into the AFM. Part 25 addresses building an aeroplane which, ultimately, gets onto the aerobridge (using a bunch of other rules) for the pilot to use. Part 121 largely tells the pilot (operator) what he may/may not do from that point in flying from A to B.
Say that a net gradient of 1.0% clears the obstacles by 35' in the second segment - I still can't use a weight higher than what would give a 2.4% gross climb gradient for the second segment.
Right. You can calculate a weight to give 1.0% net but you can't use it in practice as you are restricted (both by Part 25 AND Part 121) to whatever the WAT limit might be on the day. Just means that the pilot doesn't sweat the takeoff quite as much ...
I think it's easier to reflect in terms of
(a) gross climb approximates what the pilot should see on a reasonable day (lots of things can reduce the actual climb, eg turbulence, inversions, incorrect piloting technique, etc .. which is why we have)
(b) net climb as a calculated, conservative construct to give us a reasonable chance of missing the rocky bits on the day when it counts most. On very, very rare occasions, you might be a statistical outlier and, despite all your very best efforts .. still end up making the CFIT pages. No guarantees in flying .. only statistics.