Difference between Rightly and Rightfully

RIGHTLY vs RIGHTFULLY: ADVERB

In a correct manner; properly.
With honesty; justly.
Really.
Straightly; directly; in front.
According to justice; according to the divine will or moral rectitude; uprightly.
With honesty
According to truth or fact; correctly; not erroneously; exactly.
Aright, in a right manner, correctly
Properly; fitly; suitably; appropriately.

In a straight or right line; directly.
According to justice, duty, or the divine will; uprightly; honestly; virtuously.
Properly; fitly; suitably: as, a person rightly named.
According to truth or fact; not erroneously; correctly: as, he has rightly conjectured.

Properly; fittingly.
In a rightful manner; according to right, law, or justice; legitimately: as, a title right-fully vested.
In a righteous manner; righteously.

Precisely, Correctly, Pertinently, Genuinely, Indeed, Deservedly, Legitimately, Aptly, Sensibly, Wrongly, Understandably, Rightfully, Justifiably, Justifiedly, Justly

Correctly, Duly, Legally, Properly, Aptly, Appropriately, Wisely, Right, Deservedly, Understandably, Justly, Legitimately, Rightly, Justifiably, Truly

Truly, Judiciously, Appropriately, Wisely, Duly, Precisely, Pertinently, Genuinely, Indeed, Legitimately, Sensibly, Wrongly, Rightfully, Justifiably, Justly

Wrongly, Unfairly, Unjustly, Reasonably, Lawfully, Duly, Legally, Properly, Appropriately, Wisely, Right, Justly, Legitimately, Justifiably, Truly

We must rightly divide the Word of Truth.
The early church rightly declared Marcion a heretic.
By this they could rightly use the truth.
You have and, I think, quite rightly so.
Hast thou not sinned if thou hast brought it rightly, but not rightly divided it?
It is quite commonly held that whenever one thinks one is acting rightly, one is acting rightly.
We do not act rightly because we have virtue or excellence, but we rather have those because we have acted rightly.
Therefore, we have learned a very simple but important lesson in rightly dividing the Word of truth and rightly understanding the Book of Acts.
Prophets of soft prosperity tied psychological to fiscal success, believing that a rightly ordered mind led to rightly ordered finances.
Americans are rightly disheartened and disappointed by the economic climate and rightly so.

He was very protective of them, rightfully so.
Rightfully so," tight end Jason Witten (FSY) said.
Him: they were keeping what was rightfully His.
They would have resented that, and rightfully so.
The lyrics are minimalist here, but rightfully so.
These charges were ultimately, and rightfully so, dismissed.
Everything is about his daughter, and rightfully so.
If he is not, she may rightfully feel that she has been mistreated, and third parties may rightfully judge him to be reprehensibly selfish.
Why are these futures not rightfully their own, although they would be rightfully theirs if they were not ventilator or dialysis dependent?
The comments are going to be roasting us for this, and rightfully so, rightfully so.