My understanding from chatting with various agents is that 1-2lbs of leniency domestically is common to account for scale accuracy, and otherwise the caps are very strict. So if your limit is 50 lbs, 51 lbs is the most I'd expect to "get away with", and I'd be prepared to pull out a random item and carry it on if questioned.

Business class passengers, and elite members on domestic flights, are allowed 70lbs rather than 50lbs of baggage on domestic flights. The elite exception does not apply for international flights, though. But I liberally use this benefit to travel with my heavy rolling toolboxes for work, and it's gotten Delta business over competing airlines for all my work travel as a result even when fares are way higher.

International baggage allowances are particularly strict, and sometimes are constrained by baggage handling rules at the destination airport or by cargo/weight and balance type issues. I wouldn't expect any leniency when traveling internationally, even with status.

For carryons, I've never once seen Delta weigh a carry-on bag. Sometimes, partners operating checkin will, however (like KLM or Air France in airports in Europe), so if your trip involves a partner airline I'd take carryon weight a little more seriously.