The Forsworn, Eltrys explains to you, used to rule the Reach. The group was driven out of Markarth by Ulfric Stormcloak and his men around two decades ago, but although they no longer rule the area, they’ve been lingering around since. For the entirety of that time they’ve been causing trouble, effectively doubling the degree of bandit raids in the region by tackling many of the same targets as bandits, though for the opposite reason- rather than seeking to take material wealth for themselves, they seek to destroy the wealth of those who have the Empire’s sponsorship as ‘legitimate’ rulers of the Reach.
Eltrys’ own involvement is quite sincere, though- as he explains to you, Eltrys’ father used to own a mine in the area. According to him this is very unusual for a Nord, and only became rarer when his father was killed. The man explains that everyone knew that the attacker was one of the Forsworn, but nothing was done about it- so he devoted himself to ferreting out the Forsworn and whatever is going on with them. Recently, though, he got married and his wife is with child, prompting him to give up his investigation for the sake of his family. He’s uneasy with this, though, as the spectre of his father’s murder is still hanging over his head and piquing his curiosity and thirst for justice.
This is all the information that Eltrys has, so it’s up to you to move on the next few items- finding out about Margret and finding out about Weylin.
The fastest piece of information for you to reach (though the harder of the two to get) is the information on Margret. You’ll need to head to the Silver-Blood Inn, right by the front gate of Markarth and the scene of the attempted (or successful) murder.
If Margret is still alive, she’ll be sitting by the fire in the main room of the Inn, trying to calm herself. You can talk to her here, but there are several issues. First off, she knows nothing about Weylin at all- she assumes he was a local, but that’s all she’s got. Similarly, all she recalls about the attack is what you saw- she was at the jeweler’s stall trying to buy a necklace when the man came up behind her, announced the Forsworn, and attacked.
The real point is to find out what she’s doing- and that can be difficult. You can attempt to persuade, intimidate, or bribe her- if you’re successful, she’ll admit that she’s afraid she’s losing her touch. As it turns out, she’s a spy, here on behalf of General Tullius of the Imperial forces. Her purpose here is to investigate the Silver-Blood family that own large portions of Markarth, and specifically the local silver-generating center, Cidhna Mine. She is supposed to be trying to buy or steal the deed to the mine so that it can be held by the Imperials, but she’s come to the conclusion that ‘that’s not how things work here’. Particularly, she relates this to the attack- for whatever reason, she’s sure Thonar Silver-Blood is behind the attempt on her life. How and whether he knows her purpose here, she is uncertain.