This isn't a one way street though. The money a guy may agree to in one location/team is not necessarily the same money that it would take another team to sign him. The Bears could very well have offered or expressed a willingness to pay more - that doesn't mean he has to take it.
For example, no income tax in Florida means he can take a little less for a team in Florida and still clear more than he would in Chicago or for a California team.
Likewise, after spending years in New Orleans and in the south...he may not have wanted to go up to the north unless there really was no other option. Having lived in the south for many years myself, I can attest that it is a mental hurdle to overcome to be willing to move back to deal with things like the cold and snow.