I have a Tier 2 Visa that expires on June 2nd. This is my initial trip in my opening 30 day window and due to weather delay's in the states, I might arrive on June 3rd. Do I have options to explain my situation? Or do I need to start over?
You must not arrive in the UK outside of the validity of your entry vignette. I do not believe that you will be granted entry on the basis of your Tier 2 visa if you arrive even only a day late. UKVI makes clear the onus is on the applicant to ensure they arrive in the validity period, so travelling to arrive on the last day was always going to be risky.
However, all is not lost. You don’t need to apply for a new Tier 2 visa. You need to apply for a “transfer of conditions” to get a new entry vignette with a new validity period. Assuming you are applying in the US, this will cost $204.