I’ve loved reading this conversation. Thanks for this prompt, @Carson!
There are so many dimensions to perceiving generosity…or lack thereof. As you both have said, much of it depends upon one’s expectations as well as perspective on a given situation. If one expects nothing from anyone, then one could view receiving anything good (no matter how small) from someone as an act of generosity – ala Chesterton. I admit I tend to function like this…expect the worst so that anything “nice” is a bonus. Pleasantries are unexpected, which make them more pleasant. I expect this comes from, among other things, my Reformed theological formation and its emphasis on human depravity.
But, really, what is “generous”?
…liberal in giving or sharing
…free from meanness or smallness of mind or character
…rich or strong in flavor
syn: abundant, fertile, ample, magnanimous
For me, a tangential question to Do you experience God as generous? is How do you interpret/understand the with-holding or withdrawing of God? For, we do not have a vending machine or a genie-in-a-bottle God. He does not have to give us what we ask. God cannot be controlled by us.
@alison mentioned one of the more moralistic interpretations: God is with-holding because you are not worthy…you’ve done something wrong, therefore you have lost your “right” to health. Or perhaps you haven’t exercised enough “faith” in claiming your “right” to health. You’ll probably have to explain a bit more, Alison, because my theological frame was the exact opposite! The only “right” that humans have is the right to hell. And from that perspective, anything God would stoop to (no doubt, reluctantly) give is “generous”. Basically, God is “generous” to us for his own sake, not ours.
But in the definition above is the word liberal. Liberality connotes a freedom. Liberal giving/sharing is done freely, non-transactionally. He gives us things for our sake, first, then for the sake of others. It’s both-and, not either-or. (So much of evangelical theology is “You don’t matter. God blesses you for others’ sake.”)
So, how do I interpret and engage with both God’s generosity and with-holding, silence, mute-ness? Where I used to think that I needed to do more (or better) to earn God’s generosity, I now view the silence as an enigmatic invitation…much like what both Alison and @lakshmi have said.
I can remember being at a week-long camp one summer, and we were on the “treetops” or “high ropes” course, probably 30-or-so feet in the air. There were counsellors at every “base”, who would transfer our harnesses in between “challenges”. I remember struggling on one particular challenge, and as I made my way toward the next base, I stretched out my hand to the counsellor at the base and said, “help me”, wanting him to pull me up onto the platform. This guy (who was very kind) just sort of looked at me and where I was and said encouragingly, “You’re fine. Come on.” So I did…and I was fine. 
Sometimes, I feel like that is God with me. I reach out my hand and say “help me”, thinking that the faster he helps me (blesses me, gives me what I need to do the job) the faster I get to wherever he wants me and the better I can do the job. Everyone wins.
But, perhaps, God doesn’t want me to just do a job for him, like I’m merely a cog in a machine. Perhaps he also wants to grow me, to expand me, to challenge me? Perhaps he also desires my engagement with the whole process? Perhaps it’s not about trying harder to be better, but persevering…keeping on? Perhaps a priority of his is not efficiency but my creative expansion…and, consequently, the expansion of me in His Kingdom…and, from there, the expansion of the Kingdom as a whole. (I just read the Parables section in Matthew this morning, so the conceptualization of The Kingdom is fresh on my mind.)
So, for me, the generosity of God that I have more recently discovered is his relational generosity…the generosity and invitation of a creator’s heart. I am not an alien, external threat to God’s creation, I am a loved part of the internal process of God’s re-creation. Though I recognize that, as a part of the process, I can intentionally or inadvertently work against God (Mt. 12:30), I know that part of his generosity comes in the form of showing me how I am scattering rather than gathering with Him .