When Vader killed Padme in anger he lost his reason to live, he'd betrayed the Jedi order (using Palpatine's fictitious uprising as an excuse) and committed murder to increase his power and gain the Sith Lord's trust.

No doubt up until this point he had ambitions of saving Padme, reforming the republic with them at it's head and giving her everything. A dark and twisted devotion to her.

After her death he no longer had these motivations, I believe the fall to the dark side is very much about self deception and finding justification for your actions - after all everyone is the hero of their own story! He blamed Padme's death on the fact she'd betrayed him (bringing Obi Wan to kill him), the betrayal was then cemented when Obi Wan crippled him and left him for dead.

In his mind he'd gone to great lengths for the people he loved, these very people had then betrayed him. He'd been left alone with a crippled body and nowhere to turn... except to the man who'd rescued him and who had tried to help him save Padme - Palpatine.

The best way to put it, I think, is that Vader's spirit had been broken. The combination of succumbing to the Dark Side (and doing unspeakably evil deeds in its name), the destruction of his human body, and Padme's death all contributed in pushing Vader so far into the Darkness that he was barely human anymore. In Episode IV, Obi Wan describes Vader thus:

"He's more machine now than man. Twisted and evil."

Except for a tiny sliver that resurfaces at the end of the original trilogy, all humanity and goodness had been squeezed out of Vader, and all that was left was pure evil that the Emperor used to great effect.

Vader had nowhere else to go, and no one else to turn to.

Family:

Father

He didn't know who his father was, or if he even had a father.

Mother

His mother, the only real family he ever knew, was dead.

Step-Family

He had only met his step-father and step-brother once, for a few minutes, and hadn't left on very good terms with them.

He had no family left, aside from a step-brother and step-father he had only met once for a day or so, and he didn't seem to care for either of them.

Friends:

Anakin had very few friends.

Obi-Wan Kenobi

Obi-Wan was certainly his best friend, but Obi-Wan had just chopped off both Anakin's legs and one of his arms, then left him to die on a volcano. That bridge had clearly been burned.

Padme

Padme was also his friend, but she was dead.

The other Jedi

The other Jedi had been allies and acquaintances, but he had personally killed dozens of younlings, participated in the murder of Mace Windu, and abetted the Emperor's plan to murder all the rest. The only survivors we know of are Yoda and Obi-Wan. We've already dealt with Obi-Wan; it is unlikely that Yoda would be any more conciliatory than Kenobi was.

Jar-Jar Binks

He might also have considered Jar-Jar a friend, but we don't know whether Jar-Jar would accept Anakin after all the atrocities he'd committed, or even how Anakin would have felt about turning to Jar-Jar after Padme's death. Speaking for myself, however, I'd rather die than spend five minutes with that infuriatingly annoying, blithering amphibious idiot.

He had murdered dozens of his friends, helped kill another, been mutilated by his best friend, participated in the plot to kill all the others - which was so successful that only two survived - and contributed to the death of his wife.

Places:

Tatooine

Anakin had spent most of his life as a slave on Tatooine, and grew to despise it.

I don't like sand. It's coarse and rough and irritating and it gets everywhere.
- Attack of the Clones

Coruscant

After that, he lived at the Temple on Coruscant. The Jedi who ran the temple were now dead, some by his hand, and the Temple had become Palpatine's palace. Coruscant is actually where he set up his primary residence as Lord Vader.

Naboo

His happiest days were spent on Naboo with Padme; returning to Naboo after her death would have been agonizing for him.

Of the places Anakin had spent a significant amount of time, none were particularly inviting now. He despised his true home - Tatooine, and he was too grief-stricken to revisit the place he'd been happiest - Naboo. On top of this, if he had chosen to abandon Palpatine after all that had happened, there wouldn't be a safe place for him to go - Imperial agents would hound his every step, an eventually kill him.

Resources:

Before his treacherous switch to the Dark Side, Anakin had shunned material wealth, as was expected of all members of the Jedi Order. The Jedi were supposed to own only some clothing, a lightsaber, and, perhaps a few small personal items. Anakin was somewhat unique in that he also owned two droids.

Real Estate

He had none.

Money

He had none.

He had no home to go to, and no money or valuable property with which he might obtain a home. He was faced with the choice of being penniless and homeless on his own, or being incredibly wealthy and powerful with Palpatine.

As per Wookieepedia:

Overwhelmed by his despair in the belief he had killed Amidala and their unborn child, which fulfilled his prophetic dreams of her death, Vader destroyed the medical droids and severely damaged the facility through the Force. He broke his bindings on the operating table and struggled to walk under the sheer weight of his new prostheses and armor. The only purpose that remained in Vader's life was his service to the new Emperor.

Conclusion:

If he left Palpatine:

He would have no one to turn to, nowhere to go, and nothing to support himself; Palpatine would presumably hunt him down and kill him for his disloyalty.

If he stayed with Palpatine:

He would become rich, powerful, have ample opportunities to use his skills for evil, and eventually, he would have a chance to avenge what his new master had done by killing Palpatine.

First, you got your facts wrong Anakin didn't kill Padme, when she gave birth she lost the will to live entirely, her whole world fell apart. Her husband, left her and the senate and everything she worked for was gone. Anyways, the reason Vader stayed with Sidious is because he had nothing left, to fight for on the light side of the force.(I know this is a short answer.)

My feelings are that Anikan had mamy emotional issues. The death of his Mother. Not being accepted to the council, being married against Jedi order.

He was easily manipulated because of his emotional instability. And Sidious knew this.

He stayed as Vader because her had nothing left. Think about it. Did he ever have a true fight with his light saber? Did he use the force, other than a few chokes? Did he ever discuss things and feelings with Sidious as he did as Anikan?

Yeah, he knew the force, but never used it to its potential. Yeah, he could fight. ....but no one with skill. He became a wussy, who may be frightening, and knew the force, but never did anything to move himself forward, because he lost everything that was important to him.

A man with huge potential, but never capitalized on it.