I'm not sure why anyone would want a "super heavy fighter." It will be the worst of both worlds: inferior payload to a dedicated bomber/strike platform and inferior maneuverability to a genuine fighter.
It's more about the sensors and the stealth. Radar capability rises roughly linearly with a one-dimensional scaling factor. RCS rises as the square root of a one-dimensional scaling factor. Therefore, heavier aircraft have better radar to RCS ratios, and a JH-XX that's designed to be a super-heavy fighter has a strong shot of winning a stealth war in the radio band.
The assumption being made, likewise, (and this is a key point of contention between myself and Bltizo and others) is that maneuverability is nearly obsolete. You need instantaneous turn rate, which the J-20 is likely good at (and definitely will be good at with WS-15 with TVC), as is the F-35, to "jink" missiles, passing either through their kinematic tracking range or their seeker tracking range, but the game is no longer one of fighters trying to maneuver to get the others' six and shoot them down, because of the plethora of HOBS missiles that can do all-aspect work. If maneuverability still matters in this context, it's to put the enemy into your missile effective cone while remaining outside their missile effective cone, but this is taking place at further distances than a traditional dogfight and thus sustained maneuverability still matters a lot less.
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As far as a dedicated bomber / strike platform goes, a bomber by definition is not oriented toward air to air, so I don't need to discuss it. As far a a strike platform goes, strike aircraft are actually a subset of fighter aircraft to begin with, with the characteristic deficiency of strike aircraft being limited interception capability. When I am talking about a super-heavy fighter, I'm basically suggesting a strike aircraft, not a super-heavy air superiority aircraft, although likely air superiority will be one of the roles.
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The desire for a super-heavy fighter comes down to this, roughly. Stealth vs stealth is often a matter of counterstealth radars linked into EOTS / EODAS / IRST by datalinks. The counterstealth radar can detect and provide a rough area for the enemy stealth aircraft, often using a band that enemy jammers cannot profitably cover due to the size of the antennas required. Then the EODAS / EOTS / IRST can be cued and ordered to search the area, and EODAS / EOTS / IRST have longer tracking ranges than detection ranges due to the way optics work; check out any zoom lens, and you'll notice you have a trade-off between magnification, and thus sensitivity, and field of view. For the United States, the F-35 in combination with E-2D is a counterstealth + EOTS / EODAS / IRST combo. For China, you have KJ-600s and so on, alongside J-20s, or J-20s alongside ground-based / naval-based counterstealth. However, the J-20 is not a F-35. The F-35 is a strike fighter that's absolutely crippled when it comes to sustained supersonic performance; it's a much slower aircraft than the J-20. The J-20, on the other hand, is supposed to be either capable or eventually capable of supercruise. But the KJ-600, like the E-2D, is a subsonic platform, and consequently can't keep up with the J-20s.
A super-heavy fighter with a powerful counterstealth radar, on the other hand, can, allowing the J-20 to see enemy stealth fighters first and fire first through the counterstealth-EODAS/EOTS combo.
A super-heavy fighter can also do things that bombers cannot. For instance, the J-15D or whatnot is supposed to be an EW variant of the J-15D, providing jamming support to protect other J-15s. The Chinese have the HD-6, a H-6 outfitted with EW equipment as well. But if you compare the HD-6, the HD-6 is obviously, with the right electronics, going to be more powerful than the J-15D in terms of its jamming output, but it's also a lot less survivable, being a heavy bomber and thus limited in its maneuverability. On the other hand, the HD-6, due to its size, is better suited to mount low-band jamming equipment, i.e, jamming vs counterstealth radars, a capability that is difficult to achieve on the J-15D.
A super-heavy fighter, then, splits the difference between the HD-6 and the J-15D. The jamming equipment can be made larger, and thus capable of jamming counterstealth radars (to an extent), but at the same time, the platform is maneuverable, cheap, and light, and thus less vulnerable. And if it's stealth, it can simply turn off the jamming (probably having a partner take over), and exploit the massive synergy between stealth and jamming (stealth is roughly -10 dBsm requires in a 43-44% reduction in tracking range, but jamming means that you're now seeing a 90% reduction in tracking range per -10 dBsm).