Does burning fuel to get to your max landing weight violate any regulations?
This scenario isn't common but it isn't exactly rare, either. You take off with a full plane &amp; lots of fuel for holding &amp; an alternate, planning to arrive just at max landing weight. Then, due to shortcuts and/or better than forecast tailwinds, you under-burn &amp; see that you'll arrive above max landing weight.

First, the hypothesized rule in Part 121 doesn't exist. Absent the Captain's use of his emergency authority (which does NOT require declaring an emergency to invoke, but which DOES have to be reported after the fact), what you can't do is "just go ahead and land overweight." That would be deliberately violating an operating limitation on the aircraft, and that's bad.

Second, there's typically no need to involve the dispatcher... just burn the gas. Holding, or extended vectors, or an early descent, or extending the gear way early... take your pick of what works best in your situation &amp; then make it happen. Not a big deal.

Burning extra gas (really, just burning all the gas you'd planned to burn with the flight plan) is NOT a violation of anything in Part 121. On the contrary, intentionally landing overweight - in the absence of a circumstance making that the safest option - would be a violation.

Listen to ATC long enough, and you'll occasionally hear somebody ask for a delay to burn the extra gas. ATC can easily accommodate that; I've never heard it treated as if the crew is asking for something strange or suspect. Sometimes winds or shortcuts put you in that situation; it's nobody's fault, and it isn't a problem to burn the planned fuel.