Seikah

Isekai Ryouridou. 

Thank you for everything. 

The second is Dekoboko Girlish.

Edit: forgot a syllable.

Yup, it's a trap.

Himitsu no Akuma-chan.

Just look for the tensei (reincarnation) keyword.

Isekai Tensei Soudouki.

Mushoku Tensei.

Tensei Shitara Slime Datta Ken.

Gun-Ota ga Mahou Sekai ni Tensei Shitara something something.

Death March kara something.

Ore to Kawazu-san no Isekai Houriki.

The New Gate.

I recognize those eyebrows.

Hmm. At what point does a character become a 'side' character? There are many instances of two main characters existing in this dynamic. In fact, I wouldn't call Sai a side character... but I'll give this a shot anyway.

Shiori Experience probably fits best. Adorkable high school teacher who wants to play the guitar... and gets haunted by the ghost of Jimi Hendrix.

Edit: a second series I'm recommending cause it's just good: GATE. The protagonist isn't weak, but his love interest could break a country in half.

٩( ᐛ )و

You might enjoy Hoshi no Koe; it isn't exactly what you describe though. A couple is split up when the girl decides to travel space, and the boy stays behind on earth, aging much faster than the girl because Einstein's relativity is a bitch. Sadly, Batoto doesn't have chapters anymore.

Also, another story that doesn't quite fit, chapter 2 of Hotel. Each chapter is its own short story, so you don't have to read chapter one. (But you should, because it's extremely good.) 

I also thought I'd seen a different manga about this, but on contemplation, it was a Western movie. (The Lake House)

Got nothing without time travel happening first, I'm afraid...

This.

Light novels are just a genre of Japanese literature written to be comfortable to read, focusing on easily digestible story rather than beautiful prose. This is more obvious in Japanese, because kanji is a bitch.

Published light novels come with illustrations, amateur webnovels often go without. The difference between a novel and a 'light novel' should be obvious if you compare a traditionally published novel with a so-called Original English-Language (OEL) light novel. In my personal experience, the latter disregard believability and shamelessly rely on Rule of Cool to hold the reader's attention, rarely successfully.

Long/completed adventure manga are usually mainstream, so I can't really offer any hidden gems. Tower of God? Hunter x Hunter?

Two cents on realism and the other extreme, rule of cool.

There is little point in policing every minor contrivance, Shmu, it just leads to tedious retcon frenzies. This is a work of fiction, is it not? Don't cling to realism, it has long abdicated the throne. Believability is now king. Keep every absurdity on roughly the level by establishing clear rules, and trust your players to not exploit loopholes. Let's presume we're better than that until it happens. (A slightly abrupt scene transition is the least of your worries. Make some allowances for practicality.)

An example of establishing rules: Roger's armor may stop handguns, but not larger caliber rifles, e.g. snipers. It will also fail against armor-piercing shells, which might be more common now, considering supers exist. Does this not for all intents and purposes allow you to write Roger into gun-related trouble if you so desire? It's not as if the story is going to change in any meaningful way if, instead of scientifically sound kevlar, Roger's armor consists of semi-magical silk secreted by his moth-mutant mate.

#29 spots a previous employer, tries to go say hi, but 'cause he's in costume, has a reputation, and implicates acquaintances in villainy by association, they run the fuck away. Cue chase scene with upset applecarts and collateral damage galore.

Akane is pretty close. Acony.

Mathias Jude

An electronic sound announced the restoration from the back-up. Mathias reluctantly got up from his bed, leaving his sleep debt for another time. He'd missed his own bed more than he thought. The prison bunks had been of criminal quality, and his cellmate had snored – for a time.
 
His apartment was dark and disturbingly empty – the authorities had seized what they could get away with. Relentless sunlight penetrated the blinds. Afternoon, already? Annoying. Some business shouldn't be done beneath the sun. Mathias confirmed the website of Rise LLC was restored properly. Thankfully, the backup was recent enough that no major contracts had been lost. One particular assignment caught his eye. In obvious enough euphemisms, it requested a hit on a currently incarcerated target. Mathias marked it as completed. Technically speaking, it wasn't yet, but he'd take care of that in a moment.
 
Finances. Mathias loaded up his bank interface and skimmed over his accounts. The police had frozen some, but not enough to count as an inconvenience. Extravagance had never become his habit – a couple hundred bucks would see him through the month. He relocated some of the excess into the account of his parents. Dirty money, but they'd take it. His mother was weak. Kind, a wellspring of warm hugs, but weak. His father was weak in a different way – paralyzed in one half of his body, a souvenir from his heroism career. A bad joke. Living in fear of old enemies, forced to retire without a pension. Mathias wanted to spit, but remembered where he was just in time.
 
Mathias quickly checked his mail – nothing interesting from the lower security services. The more encrypted services handed him some capes wanting to sell Rise LLC their powers – people that didn't trust the Varrion-tech secured public net. Made sense. Rise LLC had a lot of customers nowadays, but it had started as a place for those uninterested in fame, or for those whom fame worked against. Mathias put them on the website.

He stretched, physically and mentally, rousing the muscles of his power. His left hand was free, power surging within. The power from his right hand was still connected to his prison cellmate, released two weeks before him. The man wouldn't have slept for a month now. Most turned suicidal at half of that. Mathias opened his mind's eye and his vision soared, revealing a bloodied body in a small room, not even four blocks away. The man had not been found yet. His neck was broken and most of his blood had vacated his veins, coating the floor. His eyes were spinning with pain, helpless, desperate to know why in the world he couldn't die. Mathias made a face and canceled his power, allowing the man to pass on. He had no interest in watching artless torture.
 
Time for coffee, Mathias decided, pulling on some clothes. It was noisy outside – he'd read something about a festival. Might as well visit. His public persona was a whore for attention, and it would be odd to forgo the opportunity after spending a month in prison. He walked to the door and bent down to the cage by his shoes, his power reaching for the skeleton that should be inside. Nothing. They'd taken his fucking dog. Mathias swore and kicked the cage. They'd taken his fucking dog.
 
Mathias stomped out of his apartment and set off in the direction of two massive skyscrapers. The sight of them did little to lighten his mood. There was a saying about the taller one – if you can see Varrion, Varrion can see you. Probably true. It didn't concern him that much. Live and let live, his father used to say. Mathias had always been fond of the saying. It was a pity he couldn't let anyone realize just how appropriate it was for him.