Voltage drop with Microwave
Since the problem does not happen with other appliances, it sounds like this is a problem with this one circuit. You have already swapped the breaker, so that leaves:

Wire
If this is 14AWG wire/15A circuit, try a 20A circuit (which should be 12AWG wire) if you have one available. That should help generally with voltage drop, but NOT with any fizzing and crackling.

Receptacle
The receptacle itself could be bad, and is easy to replace. But more commonly it isn't actually bad but rather has bad connections.

Connections
This is the most likely source of the problem. A bad connection (typically a back stab connection, but can also happen with a screw connection that is coming apart) can cause voltage drop (due to less wire connected than there should be, making that connection a limiting factor in the circuit) as well as other more serious problems (fizzing &amp; crackling are not just noises).


Get this fixed before you have a fire!
This is a classic case for AFCI - Arc Fault Circuit Interrupters. They are required in many circuits now but not required in old circuits unless you change things. However, they are also typically not required in kitchens because there the emphasis is on GFCI. In any case, an AFCI &quot;listens&quot; for the type of problems you describe due to bad connections, frayed insulation and other problems.
I would start with the receptacle. I would put in a GFCI unless the circuit is already protected by a GFCI elsewhere (in which case I would install a new regular receptacle). Don't use the back stab connections. Strip a little (not too much - don't want to cut off too much of the wire) fresh wire if there is any sign of damage - pitting, burn marks, etc. - and connect the new receptacle. If that doesn't solve the problem, check and reconnect/replace any other receptacles on the same circuit. If that doesn't solve the problem then you may have a wiring problem inside your walls which would generally require professional help.