My chief interest is photography, sightseeing, history and heritage. Not into beaches and relaxation. Suppose I can spend 2 days in each of Trinidad, Tobago, Grenada, Barbados, St Vincent, St Lucia, Dominica, Guadeloupe and Martinique, which 2 islands among these should I spend a few more days?
Thanks.

TWC, I recognize you from Charles' MTP site. I just returned from a trip to South America (the three Guiana), and I had stopovers in Barbados, Trinidad and Tobago. I haven't (yet) been to any of the other islands you've listed. In fact, I think they are the only islands I haven't yet visited or have plans to visit.
If you rent a car, as I did, you can see a lot of Barbados in one full day. Trinidad is interesting, especially if you are interested in birds (I'm not a bird watcher, but I spent a very enjoyable day at the Asa Wright Nature Centre, where I was able to take some great photos). You may want to only spend a few hours in Tobago -- its mostly known for beaches and relaxation. I flew over on Tobago Express (I think its around US$49 for a roundtrip ticket between Trinidad and Tobago), and I spent several hours on the beach and eating (crabs and dumplings) at Store Bay (you can walk to the beach from the airport in under 10 minutes).
I arranged thru the Asa Wright Nature Centre for a drive to take me on a tour of Port of Spain -- lots of history and heritage, but probably not the safest city to wander freely, so I was thankful to have the car and driver. If I can find your email from your website, I'll forward you a link to some photos from that trip.
Definitely St. Lucia. After that, it's kind of a close call between Dominica, Guadeloupe and Trinidad (assuming you are willing to do a little hiking). All 4 of these islands have lots of natural beauty. Out of those I'd probably go with Dominica though. Here's the link to another post I had that tell you about some of the highlights of those islands.

With that kind of itinerary (2 days in each place) you will spend most of your time waiting in airports - not fun.
I'd recommend you scale back your ambitions and spend one week in each of Grenada, Barbados and St. Vincent. The inter-island air connections are pretty good. Although their cultural heritage is much the same, they are very different in terms of photographic opportunities,
Alternately, Dominica, Martinique and Guadeloupe are another (French-speaking) grouping with relatively easy inter-island connections by ferry and air - again, tho sharing the same cultural heritage, they are each quite different, especially Dominica
I agree with curiousx: Two days in any one location wouldn't allow much opportunity for sightseeing of any kind, and I think would be exhausting besides.
I haven't been to most of the islands on your list, but I have been to Trinidad and Tobago. Since beaches aren't of any interest to you, I suggest you skip Tobago and spend at least a few days on Trinidad. There's a sizeable Indian population there, so there are some cultural sights you'd probably find interesting. You might also want to visit "Pitch Lake" - it's one of only two or three asphalt lakes in the world, and is quite a sight to see. No, it's not pretty (it is asphalt, after all), but it's well worth seeing.
Trinidad is also famous for its Scarlet Ibis birds, and there are all kinds of boat tours to go out and seem them. However, I went on one of those tours and I can't recommend them. It's a pleasant outing and all, but the boats stay so far away from the birds that the naked eye doesn't see much more than scarlet blobs. It might be worth your while only if you have a seriously powerful telephoto lens on your camera; otherwise, I'd give it a miss.