You have written, “The person whose assurance is weak can take comfort from the knowledge that if they weren’t saved, they wouldn’t be worried about it.” Is there any Scriptural basis for this?
Have you ever met a confirmed non-believer who was worried about not being saved? As soon as a person begins worrying about it they are well on their way to the cross because their discomfort is the conviction of the Holy Spirit drawing them. John 16:8 says the Holy Spirit will convict the world of guilt in regard to sin, and John 16:13 says He will guide us into all truth.
Believers who are worried are either feeling the Holy Spirit’s conviction, in which case the remedy is confession (1 John 1:9), or they’re feeling Satan’s condemnation, which can be cured by applying James 4: 7. Submit yourselves, then, to God. Resist the devil and he will flee from you. Remember, There is now no condemnation for those who are in Christ Jesus (Romans 8:1).