DIAGNOSIS Sticky or resistant door closure is almost always caused by a buildup of grease and grime on the door latch hooks (on the door) and the corresponding strike plates and switches inside the door frame.
FIX 1) Unplug the microwave. 2) Mix a solution of warm water and a degreasing dish soap. 3) Dip a cotton swab or small brush (like a clean toothbrush) into the solution, wring it out so it's damp, not dripping. 4) Carefully clean the three small metal hooks on the top and sides of the door. Then, look inside the door frame and find the slots they hook into. Clean those slots and the small plastic/metal switch levers you can see. 5) Wipe everything dry with a clean cloth. 6) Let it air dry fully, then test the door action. It should swing smoothly and click shut without force.
IF THAT DIDN'T WORK If cleaning doesn't help, one of the door interlock switches (the safety switches that click when the door closes) might be mechanically failing. You can sometimes hear if one isn't clicking. This is a safety-critical repair that requires a technician, as the microwave must not operate with a faulty door interlock.
HEADS UP Never lubricate the latch mechanism with oil or WD-40. It will attract more dust and grime, making the problem worse. Only clean with mild, dry, or lightly damp methods.