I realize that for need aware colleges, asking for financial aid reduces one’s chances of admission. However, does the amount of aid needed factor into the equation at all? In other words, do applicants that need smaller amounts of aid have better chances of admissions than those that need more, assuming all other factors are equal? Thanks in advance 
Yes, it does. For instance Reed is need aware at the end of its admissions timeline due to limits on funding. They will pick those students who they can afford to fund.
Yes. For example, Tufts first does a need-blind admission process and then compares the tentative financial aid expenditure against the budget. Then they will replace the last admitted FA-needing applicants with full-paying applicants until the budget is balanced.
At need aware schools…asking for aid doesn’t matter at all. What matters is how MUCH aid you qualify for. If you apply for aid, but your family contribution is the full cost of attendance, you won’t qualify for aid…and that is what admissions will get.
Thank you all for your responses!