“How is it weak?”
Russia was already committed in Syria at the time of the airplane bombing, and didn’t need an excuse to commit. They also don’t seek to take military action against Egypt. I don’t doubt that Putin has domestic political problems, but stopping Egyptian vacations for Russians makes them worse. I know a few Russians, and their most popular low-cost vacation destinations are (1)Turkey and (2)Egypt. Now that both of those destinations are ruled out due to the Syrian adventure, Putin has a serious domestic morale problem to deal with. I’m not a Putin fan, but I don’t think he blew up his own plane under these circumstances. Under other circumstances he is certainly evil enough to do it.
The loss of Turkey and Egypt as vacation destinations is a loss for the Russian people, not for the Pu’s regime. To him, quite the opposite, growing isolation of the people is another brick in the USSR 2.0 edifice. Remember that the USSR was very dependent on restricted travel.
Domestic anger and the sense that the country is under attack is also a gain for Pu.
The motives — I enumerated most of them already: not so much to justify his Syrian campaign, but to make it look defensive in nature, to seek quid-pro-quo with the West over Ukraine by gaining western sympathies, enlarge the foothold in the Middle East, and to expand the arms sales.