But remember that too much weight can bog down the lawn tractor. Find the ideal weight that the lawn tractor can handle AND that can do the job effectively.

When aerating, I like to go over the entire area more than once. Aerate the entire area once, then remove the plugs and aerate again. I try to alternate the direction for the second pass.

Is your soil hard? That is usually why people think they need to core aerate. Someone told you your soil was "compacted" and you needed to aerate. I'm going to suggest that your soil is not truly compacted but it is hard. Compaction and hardness happen for different reasons. Core aerating happens to address neither problem, but it really looks good on paper...until you compare it to almost any alternative. The alternative I've been using for just over 2 years now is to spray with any clear shampoo. Spray at a rate of at least 3 ounces per 1,000 square feet and follow that up with an inch of irrigation or rain. Then repeat in 2 weeks. Your soil will then become soft every time you water it and harden up again as watering day approaches. That is what should happen.

If you decide to ignore that and do it the hard way, then I would suggest running over it from every compass point. NS, EW, SN, WE, and all the points in between. Then when you are finished, water it and water it like you were trying to fill up all the holes you made. The idea is to get as much deep moisture as you can get. And the idea behind both of these approaches is to get water deep in the soil for a long time so the beneficial fungi in your soil have a chance to repopulate. Once they do, then your soil will become soft when wet and hard when dry.

Gweedo - If dish soap was an option, I would have specified dish soap. The reason I specify shampoo is simply so people will not be tempted to use dish soap. Before they put antibacterial agents in dish soap we used it all the time, but no longer. Use any clear shampoo.