When using the font modifier, set a weight to the font you're passing.

For example, if you want to use one of the default text styles (which I recommend, since they adapt to the user's Dynamic Type setting), you can do it like this:

Image(systemName: "arrow.right")
.font(Font.title.weight(.ultraLight))

If you want to specify a font size, you can do it like this:

Image(systemName: "arrow.right")
.font(Font.system(size: 60, weight: .ultraLight))

For UIKit, symbols can be configured as follows:

UIImage(systemName: "arrow.right",
withConfiguration: UIImage.SymbolConfiguration(pointSize: 16, weight: .bold))

SwiftUI 1.0

I just wanted to also mention how to change the weight along with a custom font size.

HStack(spacing: 40) {
Image(systemName: "moon.zzz")
.font(Font.system(size: 60, weight: .ultraLight))
Image(systemName: "moon.zzz")
.font(Font.system(size: 60, weight: .light))
Image(systemName: "moon.zzz")
.font(Font.system(size: 60, weight: .regular))
Image(systemName: "moon.zzz")
.font(Font.system(size: 60, weight: .bold))
}

UIKit SWIFT 5.x

To set their attributes: create a configuration then pass it in as a parameter:

let imageConfig = UIImage.SymbolConfiguration(pointSize: 22, weight: .black, scale: .large)
let image = UIImage(systemName: "delete.right", withConfiguration: imageConfig)

UIKit -- Swift 5 -- Xcode 11

If you only want to set the weight (so you don't mess up auto icon sizing), do this:

let configuration = UIImage.SymbolConfiguration(weight: .semibold)
UIImage(systemName: "trash", withConfiguration: configuration)

You can also wrap the Image with Text. With that you can use and assign the fontWeight() to Text:

Text(Image(systemName: "xmark"))
.fontWeight(.semibold)

Xcode 13.4, Swift 5.X

import UIKit
import SwiftUI




public extension Image {
    

@available(iOS 13.0, *)
static func buildSystemImage(named systemName: String, weightConfiguration: UIImage.SymbolWeight) -> Image? {
guard let imageConfig = UIImage(systemName: systemName, withConfiguration: UIImage.SymbolConfiguration(weight: weightConfiguration)) else { return nil }
return Image(uiImage: imageConfig)
}
}

Usage:

if let systemImage = Image.buildSystemImage(named: "arrow.left", weightConfiguration: .semibold) {
// Your code.
}

For iOS 16 you can use fontWeight() directly on the Image().

Image(systemName: "chevron.right")
.fontWeight(.semibold)