EasyJet is my preferred budget airline in Europe so I tend to fly with them one or more times each year. As Ed mentioned, their policy of one item of cabin baggage is strictly enforced. Cabin baggage has to meet sizing requirements, but there are no weight limits (however passengers are expected to lift items into the overhead bins on their own, as the flight crew won't be doing that).
I've never seen them make an exception with the one bag rule. I've seen some passengers place their "personal item" such as a purse inside their carry-on, and then remove it when they're on board the aircraft.
If you're going to be checking luggage and the item will be over their allowable weight limit, it's cheaper to pay for the higher weight at the time of booking rather than at the gate. Also, if your budge will allow I'd recommend paying for the speedy boarding as it makes the process easier.