Welcome to the forums. I can hear the hurt and frustration in your post. I'm sorry that you feel so low at the moment.
So your relationship ended a little while back, but you had your children, so you were easily able to distract and suppress. Now that your children have left it sounds like your heart and soul want to finally grieve. The end of a relationship is just like any other loss. We have to go through the grieving process. Have you considered getting some support with this? It might be helpful to see your GP and perhaps even get a referral to a Psychologist or counsellor.
Sadly with depression the mind gets hooked on everything negative, and the positive stuff seems very cloudy and distant. Hence you say you are lacking in motivation to do anything. The good thing is that you've managed to keep working - this can be a good distraction, even if it it is just to pay the bills.
I'd suggest one thing at a time. If I re-list all the things you don't do/have then I think we can assume they're all the things you wish you were/had.
"I don’t socialize" - I guess this comes from networking and getting a group of friends so that you feel you have places to go.
"I don’t have any friends" - What sorts of things do you enjoy? My parents are in a similar situation to you. My dad has joined a swimming group, and my mum joined a knitting group and a book club. There are plenty of ways to meet people.
"I don’t visit family" - Is it possible to get family to visit you? Hosting afternoon tea is relatively simple, and will give you a chance to socialise.
"I don’t visit my grand kids" - Three weeks ago I asked my sister if my nephews could take a day off school so that I could hang out with them. I don't think your daughters will think you are interrupting their lives. They love you, of course they want you to visit your grand kids. And being around children can be very helpful for depression.
"I'm overweight" - If you want to change this, you'll need to do the hard work. Look at your eating habits. Decide on a form of exercise that you enjoy. Perhaps yoga, or walking, swimming? Exercise with a group, even if it's through your local community centre, this will give you another opportunity to meet people.
Depression wants us to withdraw, isolate, feel lonely, and unlovable, beating it means not giving in to it's desires. This isn't easy which is why I suggest getting some extra professional support.
I hope to hear back from you.