Hi, I'd like to help you with your question.
If this is a new behavior for your sister, she may need a checkup with her doctor. Changes in behavior, especially at her age, may be due to physical causes such as dementia, Alzheimer's or Pick's disease, which is a deterioration of the frontal lobe. If your sister will not go herself, consider going with her or have someone she is comfortable with go with her. The doctor needs to be aware she is acting like this so the evaluation can be accurate.
If she is cleared medically, then this becomes a psychological issue. Is there a reason you feel she is crying and clingy? Did something occur in her life recently, such as a death or major change of some sort (moving, health problems, etc). In that case, she may be depressed and not able to handle her emotions as well as she normally does.
Would she be willing to talk to either a counselor or a pastor? If she is, she can talk to her doctor for a referral. Or she can search on line for a therapist at http://therapists.psychologytoday.com/rms/.
In coping with her behavior, you may want to try to suggest she stay busy, if she is not already. Help her find a group to join, a new hobby, or suggest a short vacation to visit other family or friends. She may need a change to help her feel better.
Also, try to not bring up her behavior directly. Instead of saying she is too clingy, suggest she help you in some way when she is around. Give her a chore or ask her help with something that needs done. Or be ready to leave your home when she has overstayed her welcome. That way, you at least can control the situation somewhat until it can be resolved.
I hope this has helped,