You should file for a formal custody agreement, or at least consult an attorney to determine the likelihood of getting more time. There is much to be considered, and it would seem you may have to sacrifice days of contact to actually get more calendar time (as in, you may lose a day or two, but get 3 consecutive days or something).
Since there is no agreement in place currently, she is entitled to ask for child support--regardless of whether you spend one minute or all week with your son--the two are not related in any way.
Some states have guidelines which set support relative to a certain percentage of parenting time, in which case, your ex g/f could easily seek to reduce the time to maximize support.
Given the existing level of contact (5 of 7 days) it would be very challenging for her to seek to limit that or get ordres which reduce the existing time. as stated, you could increase time but lose days of contact in exchange for more overnights.