Ahhh Bishadi is here: I wondered why this thread was still going
Probably the thing to do here is to avoid confusing the map with the territory - there are a lot of different models for gravitation, each addressing important aspects.
Newtonian Gravitation kicks the whole stuff off and the model works for pretty much everything you will ever see in your normal life.
General Relativity starts out with the observation that a linearly accelerating reference frame is indistinguishable from a gravitating one. (Rotational acceleration, as pointed out to 2008 - go back to the start of this thread, is different.) The trouble with this is that it produces singularities in euclidean geometry ... so we just use a non-euclidean geometry in our calculations. The effect is that if we send two objects out on parallel courses, they will eventually collide. This is the behavior we get, in 2D, on the surface of a sphere ... which is why we say that space time is curved. Indeed, the maths is consistent with the mathematical concepts related to curvature, only in 4 dimensions .... we can forgive people who find this hard to imagine.
General Relativity manages to reduce to Newtonian gravitation in the case of small accelerations and it is quite easy to show. You'll find it in the early chapters of any recent text-book on gravitation. The math is not too hard at that stage, you don't even need tensors. Go look.
In this model, gravitation is still a property of mass, but manifests as a measurable curvature. As a result, you can deduce the mass of an object by measuring the space-time curvature near it. Which is what we normally do for very big things like planets. However, if you are very careful, you can attempt the Cavendish experiment - which does this for very small objects.
A telling reason this curvature idea works better than newtons is that photons, massless, are still affected by gravity (and differently to the path if you used the mass-energy relation to compute the photons "gravitational mass"). Now I know that Bashadi does not like photon models - in which case it is even worse as the EM fields are also affected by gravity and you don't even have the handy "particle" to blame. If you don't like the idea that space-time is "actually" curved, consider it a metaphor arising from the math - much as some predator-prey models have elliptical math - and blame, instead, the differing reference frames.
Gravitons and stuff are parts of attempts to unify quantum mechanics with general relativity. There are a bunch of different ways to deal with this which are all unsatisfactory in some circumstances. You'll never run into the situations they involve in normal life.
Even in normal QM, general relativity is added as a perturbation on the weightless form of the math ... just to get the fine detail out. In this context it is a very small effect.
From the POV of the OP - the question is adequately answered by resolving confusions around Newtonian gravitation.
As for what gravity actually
is - it is the name given to label a set of phenomena. Mainly we are talking about how come objects stick to the Earth, as OP observed they should be slung off. But, centrally, and publishing this was Newtons important contribution, is that two masses initially at rest wrt each other are observed to accelerate towards each other. Please please please do not confuse the map with the territory. As soon as you start talking about the fundamental nature of the Universe you enter a work in progress -
nobody knows: live with it.
